some recursive formulas for selberg type integrals a set of recursive relations satisfied by selberg type integrals involving monomial symmetric polynomials are derived generalizing previous results in aomoto 1987 siam j math anal 18 545 49 and iguri 2009 lett math phys 89 141 58 these formulas provide a well defined algorithm for computing selberg schur integrals whenever the kostka numbers relating schur functions and the corresponding monomial polynomials are explicitly known we illustrate the usefulness of our results discussing some interesting examples

a selberg integral for the lie algebra an a new q binomial theorem for macdonald polynomials is employed to prove an a n analogue of the celebrated selberg integral this confirms the mathfrak g rm a n case of a conjecture by mukhin and varchenko concerning the existence of a selberg integral for every simple lie algebra mathfrak g

noncompact qualitative games with application to equilibria abstract in 2003 s y chang maximal elements in noncompact spaces with application to equilibria proc amer math soc 132 2 2003 535 541 obtained a maximal theorem for l s majorized correspondences in noncompact spaces in this paper we extend this result to obtain new existence theorems for qualitative games applying it we have more refined existence theorems for both abstract economies and generalized n person games than before

existence of equilibria for generalized games and generalized social systems with coordination the general existence of equilibria for non compact generalized games in which the l majorized preference mappings may not have lower semicontinuity is established it is shown that the constraint mappings may only be either lower of upper semicontinuous and the set of players may not be countable the underlying spaces are also shown to be either infinite dimensional locally convex topological vector spaces

random matrix theory the exceptional lie groups and l functions there has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number theoretical l functions one example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of l functions these connections are extended here to non classical groups we focus on an explicit example the exceptional lie group g2 the value distributions for characteristic polynomials associated with the 7 and 14 dimensional representations of g2 defined with respect to the uniform invariant haar measure are calculated using two of the macdonald constant term identities a one parameter family of l functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the seven dimensional representation of g2 the random matrix calculations extend to all exceptional lie groups

random matrix theory and l functions at s 1 2 recent results of katz and sarnak 8 9 suggest that the low lying zeros of families of l functions display the statistics of the eigenvalues of one of the compact groups of matrices u n o n or usp 2n we here explore the link between the value distributions of the l functions within these families at the central point s 1 2 and those of the characteristic polynomials z u of matrices u with respect to averages over so 2n and usp 2n at the corresponding point 0 using techniques previously developed for u n in 10 for any matrix size n we find exact expressions for the moments of z u 0 for each ensemble and hence calculate the asymptotic large n value distributions for z u 0 and log z u 0 the asymptotic results for the integer moments agree precisely with the few corresponding values known for l functions the value distributions suggest consequences for the non vanishing of l functions at the central point

on equilibria of non compact generalized games abstract a fixed point theorem is first proved from which a theorem on the existence of maximal elements for lc majorized correspondences defined on a non compact set is obtained next an equilibrium theorem for non compact qualitative games with lc majorized correspondences defined on a non compact strategy set is proved and is applied to prove an equilibrium theorem for non compact generalized games with lc majorized correspondences defined on a non compact strategy set our results generalize several previously published corresponding results

intersection theorems and their applications in general almost convex spaces abstract in this paper we extend the concept of the almost convex condition and establish an approximation property for convex continuous correspondences we use the approximation property to generalize von neumann s intersection theorems and related topics we obtain as applications some new equilibrium theorems for the existence of a maximal element generalized games and qualitative games of u majorized correspondences

equilibria of noncompact abstract economies in general almost convex strategy spaces abstract we first extend the concept of almost convex condition and establish a fixed point theorem for correspondences with convex values only on an almost convex subset for their ranges this generalizes both results of himmelberg c j himmelberg fixed points of compact multifunctions j math anal appl 38 1972 205 207 and the result of jafari and sehgal f jafari v m sehgal an extension to a theorem of himmelberg j math anal appl 327 2007 298 301 furthermore applying it we have existence theorems for equilibria of noncompact abstract economies in general almost convex strategy spaces our theorems generalize the corresponding results of zhou jianxin zhou on the existence of equilibrium for abstract economies j math anal appl 193 1995 839 858 tan and wu k k tan z wu a note on abstract economies with upper semicontinuous correspondence appl math lett 11 5 1998 21 22 in several ways in particular we answer the question raised by zhou in the reference cited above in the affirmative with weaker hypotheses

inequalities and nash equilibria abstract this paper concentrates on the problem of the existence of equilibrium points for non cooperative generalized n person games n person games of normal form and their related inequalities we utilize the k k m lemma to obtain a theorem and then use it to obtain a new fan type inequality and minimax theorems various new equilibrium point theorems are derived with the necessary and sufficient conditions and with strategy spaces with no fixed point property examples are given to demonstrate that these existence theorems cover areas where other existence theorems break down

vanishing via lifting to second witt vectors and a proof of an isotriviality result abstract a proof based on reduction to finite fields of esnault and viehweg s stronger version of the sommese vanishing theorem for k ample line bundles is given this result is used to give different proofs of isotriviality results of parshin and migliorini

a comparison theorem if x is complete these maps are isomorphisms but in general they are not this ibllows from the following standard example due to serre 4 p 232 one takes a certain ip 1 bundle x over a non singular elliptic curve and removes a curve y the result is a non singular algebraic surface u x y on which every regular function is constant h the associated complex space ua of u is a stein naanifold biholomorphic to x where denotes tl 0 4 in particular we see that in this example the comparison map o h u gv h gv is not an isomorphism the point is that in serre s example the degree of the normal bundle nr x of y in x is zero this suggests the following problem let x be an algebraic variety over c ycx a closed subvariety defined by the ideal j find sufficient conditions on the normal sheaf nr x of y in x such that for every coherent algebraic sheaf f on x y the comparison maps h x y van

quantum group structure in the fock space resolutions of widehat sl n representations we describe a complex of wakimoto type fock space modules for the affine kac moody algebra widehat sl n the intertwining operators that build the complex are obtained from contour integrals of so called screening operators we show that a quantum group structure underlies the algebra of screening operators this observation greatly facilitates the explicit determination of the intertwiners we conjecture that the complex provides a resolution of an irreducible highest weight module in terms of fock spaces

recurrence equations for the computation of correlations in the 1 r 2 quantum many body system in a previous paper the two particle distribution function and one particle density matrix for the quantum many body system with the 1 r2 pair potential have been expressed as limiting cases of selberg correlation integrals recurrence equations are derived which allow rapid evaluation of these multidimensional integrals the exact results for the two particle distribution are compared with the harmonic approximation

chern simons matrix models and stieltjes wigert polynomials employing the random matrix formulation of chern simons theory on seifert manifolds we show how the stieltjes wigert orthogonal polynomials are useful in exact computations in chern simons matrix models we construct a biorthogonal extension of the stieltjes wigert polynomials not available in the literature necessary to study chern simons matrix models when the geometry is a lens space we also study the relationship between stieltjes wigert and rogers szego polynomials and the corresponding equivalence with a unitary matrix model finally we give a detailed proof of a result that relates quantum dimensions with averages of schur polynomials in the stieltjes wigert ensemble

existence of equilibria for generalized games without paracompactness in this paper we first prove an existence theorem of maximal elements without any paracompactness then we establish an existence theorem of equilibrium points of generalized games with infinite many players and without any paracompactness by applying our maximal element existence theorem our equilibrium existence theorem answers the two questions raised by kim 6 in the affirmative

the importance of the selberg integral it has been remarked that a fair measure of the impact of atle selberg s work is the number of mathematical terms that bear his name one of these is the selberg integral an n dimensional generalization of the euler beta integral we trace its sudden rise to prominence initiated by a question to selberg from enrico bombieri more than thirty years after its initial publication in quick succession the selberg integral was used to prove an outstanding conjecture in random matrix theory and cases of the macdonald conjectures it further initiated the study of q analogues which in turn enriched the macdonald conjectures we review these developments and proceed to exhibit the sustained prominence of the selberg integral as evidenced by its central role in random matrix theory calogero sutherland quantum many body systems knizhnik zamolodchikov equations and multivariable orthogonal polynomial theory

the selberg jack symmetric functions abstract k aomoto has recently given a simple proof of an extension of a selberg s integral we prove the following generalization of aomoto s theorem for eachk 0 there exists a family sk t of homogeneous symmetric functions such that if the integrand of selberg s integral is multiplied bysk t1 tn then the integral has a certain closed form sincesk t is a renormalized jack symmetric function with 1 k we call sk t the selberg jack symmetric functions r p stanley and i g macdonald have extended many of the basic properties of the i j schur functions to the jack symmetric functions stanley s extensions of the pieri formula in a form obtained by macdonald s extension of the duality property and the combinatorial representation arise naturally in our proof we give proofs of these and other results of stanley and macdonald we give two constant term identities which are equivalent to the integration formula these results extend w g morris theorem foranand the macdonald morris constant term identity forbcn by exploring selberg s proof of his integral we give a recurrence relation outline a method for calculating the selberg jack symmetric functions and show that a constant term orthogonality relation recently proved by macdonald arises naturally we give an expansion which allows us to evaluate the normalization of this orthogonality thus giving an alternative proof of the integration formula

on the existence of equilibrium for abstract economies abstract in this paper several existence theorems for abstract economies have been established they are natural modifications strict generalizations when strategy spaces are metrizable of the main results of yannelis and prabhakar 23 tulcea 22 and ding kim and tan 10 for infinite dimensional casas for the finite dimensional case we show that the topological conditions on correspondences in shafer and sonnenschein s result 20 can be much weaker along the proofs several propositions are established which are of independent interest we also show that many existence results in fixed point theory maximization theory and generalized quasi variational inequalities can be encompassed