on the capacity formula for multiple input multiple output wireless channels a geometric interpretation the capacity of multiple input multiple output mimo wireless channels is computed for ricean channels the novelty is a geometrical ray tracing interpretation of the mimo channel capacity formula to find array geometries which greatly enhance channel capacity compared to single input single output siso systems

canonical bases and affine hecke algebras of type b we prove a series of conjectures of enomoto and kashiwara on canonical bases and branching rules of affine hecke algebras of type b the main ingredient of the proof is a new graded ext algebra associated with quiver with involutions that we compute explicitly

duality for ext groups and extensions of discrete series for graded hecke algebras in this paper we study extensions of graded affine hecke algebra modules in particular based on an explicit projective resolution on graded affine hecke algebra modules we prove a duality result for ext groups this duality result with an ind res resolution gives an algebraic proof of the fact that all higher ext groups between a tempered module and a discrete series vanish

robust stabilization of interval plants using lead or lag compensators abstract a lead or lag compensator robustly stabilizes a family of interval plants if and only if it simultaneously stabilizes the vertex plants

the exotic robinson schensted correspondence abstract we study the action of the symplectic group on pairs of a vector and a flag considering the irreducible components of the conormal variety we obtain an exotic analogue of the robinson schensted correspondence conjecturally the resulting cells are related to exotic character sheaves

homological algebra for affine hecke algebras abstract in this paper we study homological properties of modules over an affine hecke algebra h in particular we prove a comparison result for higher extensions of tempered modules when passing to the schwartz algebra s a certain topological completion of the affine hecke algebra the proof is self contained and based on a direct construction of a bounded contraction of certain standard resolutions of h modules this construction applies for all positive parameters of the affine hecke algebra this is an important feature since it is an ingredient to analyse how the irreducible discrete series representations of h arise in generic families over the parameter space of h for irreducible non simply laced affine hecke algebras this will enable us to give a complete classification of the discrete series characters for all positive parameters we will report on this application in a separate article

robust controller synthesis using kharitonov s theorem the authors present a method based upon kharitonov s theorem for synthesizing robustly stabilizing feedback controllers the approach is based upon a multiple plant model formulation with a quadratic cost functional sufficient conditions are obtained for characterizing robustly stabilizing static output feedback proportional controllers for mimo multiple input multiple output plants with denominator polynomial uncertainty

homology of the zero set of a nilpotent vector field on a flag manifold 0 1 let x be a linear transformation of a finite dimensional vector space v the configuration of flags in v which are fixed by x has rather remarkable properties when x is unipotent though this case is especially interesting the proper generality in which to study such configurations is in the theory of reductive algebraic groups where their definition can be reformulated in the language of borel subalgebras as follows let g be a connected reductive group over c with lie algebra g and let n e g be a nilpotent element let q be the variety of all borel subalgebras of g and let

simultaneous stabilization of single input single output discrete time systems the problem of finding one compensator which simultaneously stabilizes a family of single input single output siso discrete time plants is considered the family of plants is described by the transfer functions pz q q in q which are generated via a z transformation a number of assumptions describing the set of allowable plants are then given these assumptions include some regularity conditions on the plants and a minimum phase requirement the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c z for simultaneous stabilization an iterative computation method is provided for control design

stabilization of a linear plant via a stable compensator having no real unstable zeros abstract this paper studies the following problem under what conditions can a linear plant be stabilized by a stable compensator having no real zeros in the closed right half plane solving this problem is an important step towards to solving the problems of stabilization of linear systems via stable minimum phase compensation and simultaneous stabilization of n n 2 plants in the paper necessary and sufficient conditions are derived these conditions are completely general and therefore encompass unstable nonminimum phase plants as well it is shown that the stabilizability solely depends on the locations of real zeros and real poles of a given plant for a plant satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is also provided and illustrated via an example

an interpolated controller for stabilization of a plant with variable operating conditions this paper considers stabilization of a linear time invariant single input single output plant with variable operating conditions it is assumed that the plant is described by a linear interpolation of proper stable coprime factorizations of the transfer functions of two representative models which are defined at two representative operating points a linear interpolation of stabilizing controllers for the representative models is applied to the interpolated plant the necessary and sufficient condition for the interpolated plant to be stabilizable by the interpolated controller is presented using the nevanlinna pick theory it is also shown that simultaneous stabilizability of the two representative models is necessary for such stabilization an example is given which illustrates that the class of stabilizable plants via interpolated controllers is larger than that of plants stabilizable by fixed controllers

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations

an approach to simultaneous system design part 11 nonswitching gain and dynamic feedback compensation by algebraic geometric methods this paper studies structured uncertainty problems in feedback system design considers a compact parameterization of the space of linear dynamical systems and introduces base points and critical points as two algebraic geometric objects that have significance in sensitivity and robustness studies respectively using the nevanlinna pick interpolation theory the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one parameter family of plants a recent result due to kharitonov on the simultaneous stability of a parameterized family of polynomials leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants furthermore the author considers simultaneous pole placement of an r tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system the concept of nondegenerate and twisted r tuples of plants is introduced as the pole placement problem is studie

on characters and formal degrees of discrete series of affine hecke algebras of classical types we address two fundamental questions in the representation theory of affine hecke algebras of classical types one is an inductive algorithm to compute characters of tempered modules and the other is the determination of the constants in the formal degrees of discrete series in the form conjectured by reeder j reine angew math 520 37 93 2000 the former is completely different from the lusztig shoji algorithm shoji in invent math 74 239 267 1983 lusztig in ann math 131 355 408 1990 and it is more effective in a number of cases the main idea in our proof is to introduce a new family of representations which behave like tempered modules but for which it is easier to analyze the effect of parameter specializations our proof also requires a comparison of the c theoretic results of opdam delorme slooten solleveld j inst math jussieu 3 531 648 2004 arxiv 0909 1227 int math res not 2008 adv math 220 1549 1601 2009 acta math 205 105 187 2010 and the geometric construction from kato duke math j 148 305 371 2009 am j math 133 518 553 2011 ciubotaru and kato adv math 226 1538 1590 2011

orbit closures in the enhanced nilpotent cone we study the orbits of g gl v in the enhanced nilpotent cone where is the variety of nilpotent endomorphisms of v these orbits are parametrized by bipartitions of n dimv and we prove that the closure ordering corresponds to a natural partial order on bipartitions moreover we prove that the local intersection cohomology of the orbit closures is given by certain bipartition analogues of kostka polynomials defined by shoji finally we make a connection with kato s exotic nilpotent cone in type c proving that the closure ordering is the same and conjecturing that the intersection cohomology is the same but with degrees doubled

exact capacity expressions for dual branch ricean mimo channels in this paper we derive exact expressions for the mutual information mi probability density function and the mi cumulative distribution function of dual branch multipleinput multiple output mimo systems either two transmit tx or two receive rx antennas communicating over a ricean channel with no constraint on the rank of the line of sight los channel matrix this is done both for the case where the channel is only known at the rx and for the case where the channel is known both at the tx and the rx as an example to evaluate the expressions we employ uniform linear arrays and give expressions for the eigenvalues of the los channel matrix for the dual branch case

capacity of multiple antenna systems with both receiver and transmitter channel state information the capacity of multiple antenna systems operating in rayleigh flat fading is considered under the assumptions that channel state information csi is available at both transmitter and receiver and that the transmitter is subjected to an average power constraint first the capacity of such systems is derived for the special case of multiple transmit antennas and a single receive antenna the optimal power allocation scheme for such a system is shown to be a water filling algorithm and the corresponding capacity is seen to be the same as that of a system having multiple receive antennas with a single transmitter antenna whose outputs are combined via maximal ratio combining a suboptimal adaptive transmission technique that transmits only over the antenna having the best channel is also proposed for this special case it is shown that the capacity of such a system under the proposed suboptimal adaptive transmission scheme is the same as the capacity of a system having multiple receiver antennas with a single transmitter antenna combined via selection combining next the capacity of a general system of multiple transmitter and receiver antennas is derived together with an equation that determines the cutoff value for such a system the optimal power allocation scheme for such a multiple antenna system is given by a matrix water filling algorithm in order to eliminate the need for cumbersome numerical techniques in solving the cutoff equation approximate expressions for the cutoff transmission value are also provided it is shown that compared to the case in which there is only receiver csi large capacity gains are available with optimal power and rate adaptation schemes the increased capacity is shown to come at the price of channel outage and bounds are derived for this outage probability

all constant gain stabilizing controllers for an interval delay system with uncertain parameters a computationally tractable design method is presented which explicitly yields the entire set of all constant gain controllers which robustly stabilize a family of systems with uncertainty a desired optimal controller may then be selected from the feasible set the method applies to the class of systems where a delay element e hs with interval finite or infinite uncertainty about h is followed by a plant characterized by a rational transfer function with independent interval coefficients illustrative numerical examples are provided

sufficient conditions for generic simultaneous pole assignment and stabilization of linear mimo dynamical systems it has been shown that a generic r tuple of m input p output dynamical systems is simultaneously stabilizable pole assignable if r m p and the mcmillian degrees of the systems are not too different this result improves the currently known upper bound r spl les max m p on the number of plants in the case r spl les max m p an upper bound on the degree of the simultaneous pole assigning compensator has also been derived which improves the bound obtained by ghosh and byrnes 1983

on minimal degree simultaneous pole assignment problems in this paper we show that a generic r tuple of m input p output linear systems is simultaneously pole assignable if r m p and the mcmillan degrees of the systems are not too different we also obtain upper bounds for the degrees of the compensators which simultaneously assign the characteristic polynomials of the r tuple of closed loop systems the upper bounds are obtained for each of the two cases r max m p and max m p r m p 2002 elsevier science inc all rights reserved

a pole placement design approach for systems with multiple operating conditions the author proposes design procedures based on state space pole placement techniques for systems with multiple operating conditions this is the so called simultaneous pole placement problem first the full state feedback problem is studied in which a nonlinear local pole placement solution is proposed the design condition is formulated in terms of the rank condition of a multimode controllability matrix then the output feedback problem is approached using a multimodel controller design which is an extension of the observer design to multimode systems the design is decomposed into separated global pole placement subproblems and a local pole placement subproblem for a system with some operating conditions having modes on the j omega axis but no modes at the origin in the open right half of the complex plane stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established without any restriction on the number of inputs or outputs relations of this approach to other simultaneous control design approaches are pointed out

discrete series characters for affine hecke algebras and their formal degrees we introduce the generic central character of an irreducible discrete series representation of an affine hecke algebra using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine hecke algebras except for the types e n 1 n 6 7 8 with arbitrary positive parameters and we prove an explicit product formula for their formal degrees in all cases

the mirabolic hecke algebra abstract the iwahori hecke algebra of the symmetric group is the convolution algebra of gl n invariant functions on the variety of pairs of complete flags over a finite field considering convolution on the space of triples of two flags and a vector we obtain the mirabolic hecke algebra r n which had originally been described by solomon in this paper we give a new presentation for r n which shows that it is a quotient of a cyclotomic hecke algebra as defined by ariki and koike from this we recover the results of siegel about the representations of r n we use jucys murphy elements to describe the center of r n and to give a gl structure on the grothendieck group of the category of its representations giving mirabolic analogues of classical results about the iwahori hecke algebra we also outline a strategy towards a proof of the conjecture that the mirabolic hecke algebra is a cellular algebra

a sufficient condition for simultaneous stabilization the condition under which it is possible to find a single controller that stabilizes k single input single output linear time invariant systems p sub i s i 1 k is investigated the concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable a method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example

deformations of nilpotent cones and springer correspondences let g mathop sp 2n be the symplectic group over bbb z we present a certain kind of deformation of the nilpotent cone of g with g action this enables us to make direct links between the springer correspondence of frak sp 2n over bbb c that over characteristic two and our exotic springer correspondence as a by product we obtain a complete description of our exotic springer correspondence

the exotic nilcone of a symplectic group abstract let g be the symplectic group s p 2 n k k an algebraically closed field of characteristic 2 it acts in v k 2 n the exotic nilcone of g is the nilcone in the sense of invariant theory of the g module v 2 v the paper discusses elementary properties of the g action on the exotic nilcone

the solution of a transcendental problem and its applications in simultaneous stabilization problems a complete solution for a special transcendental problem in system theory is given one of the interpretations of this transcendental problem is the following simultaneous stabilization problem under what conditions can two linear plants be simultaneously stabilized by a single compensator having no real poles in the closed right half of the complex plane these conditions are completely general and therefore encompass unstable non minimum phase plants as well it is shown that the simultaneous stabilizability of two given plants via such a restricted compensator depends solely on the locations of the real zeros of the two plants and their difference plant in the closed right half of the complex plane for two plants satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is provided and illustrated a computationally checkable necessary condition for simultaneous stabilization of three plants is also given

ergodic capacity upper bound for dual mimo ricean systems simplified derivation and asymptotic tightness an analytical upper bound on the ergodic capacity of multiple input multiple output mimo systems is deduced with the aid of a simplified approach that relies on a fundamental power normalization given their high practical usability we are particularly interested in dual configurations where both ends deploy two antenna elements contrary to the majority of related studies where only the common case of rayleigh fading is considered our analysis is extended to account for ricean fading where a deterministic line of sight los component exists in the communication link and both ends are affected by spatial correlation in the following it is shown that the proposed bound is applicable for any arbitrary signal to noise ratio snr and rank of the mean channel matrix in fact we consider both conventional and optimized mimo configurations with equal los eigenvalues moreover the tightness of the bound is explored where it is demonstrated that as the snr tends to zero the bound becomes asymptotically tight at high snrs the offset between empirical capacity and the bound is analytically computed which implies that an explicit asymptotic capacity expression can ultimately be obtained

a vanishing theorem for dirac cohomology of standard modules abstract this paper studies the dirac cohomology of standard modules in the setting of graded hecke algebras with geometric parameters we prove that the dirac cohomology of a standard module vanishes if and only if the module is not twisted elliptic tempered the proof makes use of two deep results one is some structural information from the generalized springer correspondence obtained by s kato and lusztig another one is a computation of the dirac cohomology of tempered modules by barbasch ciubotaru trapa and ciubotaru we apply our result to compute the dirac cohomology of ladder representations for type a n for each of such representations with non zero dirac cohomology we associate to a canonical weyl group representation we use the dirac cohomology to conclude that such representations appear with multiplicity one