some reducible specht modules we wish to consider which ordinary irreducible representations of the symmetric group sn remain irreducible modulo a prime p this is the same as asking which partitions of n have the property that the corresponding specht module s is reducible over a field of characteristic p if or its conjugate partition is p regular then the answer is known 6 8 it is also known in the case p 2 7 this paper discusses some of the reducible specht modules in the case that p 3 throughout p will be an odd prime and a partition of some integer n we will prove some cases of a conjecture by james and mathas 9 given below we begin with some definitions

irreducible projective representations of the alternating group which remain irreducible in characteristic 2 abstract for any finite group g it is an interesting question to ask which ordinary irreducible representations of g remain irreducible in a given characteristic p we answer this question for p 2 when g is the proper double cover of the alternating group as a key ingredient in the proof we prove a formula for the decomposition numbers in rouquier blocks of double covers of symmetric groups in terms of schur p functions

gauge invariant lattice quantum field theory implications for statistical properties of high frequency financial markets abstract we report on initial studies of a quantum field theory defined on a lattice with multi ladder geometry and the dilation group as a local gauge symmetry the model is relevant in the cross disciplinary area of econophysics a corresponding proposal by ilinski aimed at gauge modeling in non equilibrium pricing is implemented in a numerical simulation we arrive at a probability distribution of relative gains which matches the high frequency historical data of the nasdaq stock exchange index

some reducible specht modules for iwahori hecke algebras of type a with q 1 abstract let p be a prime and f a field of characteristic p and let h n denote the iwahori hecke algebra of the symmetric group s n over f at q 1 we prove that there are only finitely many partitions such that both and are 2 singular and the specht module s for h is irreducible

character values and decomposition matrices of symmetric groups the relationships between the values taken by ordinary characters of symmetric groups are exploited to prove two theorems in the modular representation theory of the symmetric group 1 the decomposition matrices of symmetric groups in odd characteristic have distinct rows in characteristic 2 the rows of a decomposition matrix labelled by the different partitions and are equal if and only if and are conjugate an analogous result is proved for hecke algebras 2 a specht module for the symmetric group sn defined over an algebraically closed field of odd characteristic is decomposable on restriction to the alternating group an if and only if it is simple and the labelling partition is self conjugate this result is generalised to an arbitrary field of odd characteristic

the irreducible representations of the alternating group which remain irreducible in characteristic p let p be an odd prime and an the alternating group of degree n we determine which ordinary irreducible representations of u n remain irreducible in characteristic p verifying the author s conjecture from 2010 given the preparatory work done in 2010 our task is to determine which self conjugate partitions label specht modules for the symmetric group in characteristic p having exactly two composition factors this is accomplished through the use of the robinson brundan kleshchev i restriction functors together with known results on decomposition numbers for the symmetric group and additional results on the mullineux map and homomorphisms between specht modules

a model for stocks dynamics based on a non gaussian path integral abstract we introduce a model for the dynamics of stock prices based on a non quadratic path integral the model is a generalization of ilinski s path integral model more precisely we choose a different action which can be tuned to different time scales the result is a model with a very small number of parameters that provides very good fits of some stock prices and indices fluctuations

arbitrage free self organizing markets with garch properties generating them in the lab with a lattice model abstract we extend our studies of a quantum field model defined on a lattice having the dilation group as a local gauge symmetry the model is relevant in the cross disciplinary area of econophysics a corresponding proposal by ilinski aimed at gauge modeling in non equilibrium pricing is realized as a numerical simulation of the one asset version the gauge field background enforces minimal arbitrage yet allows for statistical fluctuations the new feature added to the model is an updating prescription for the simulation that drives the model market into a self organized critical state taking advantage of some flexibility of the updating prescription stylized features and dynamical behaviors of real world markets are reproduced in some detail

a path integral based model for stocks and order dynamics abstract we present a model for the short term dynamics of financial assets based on an application to finance of quantum gauge theory developing ideas of ilinski we present a numerical algorithm for the computation of the probability distribution of prices and compare the results with apple stocks prices and the s p500 index

some q analogues of the carter payne theorem we prove a q analogue of the carter payne theorem for the two special cases cor responding to moving an arbitrary number of nodes between adjacent rows or moving one node between an arbitrary number of rows as a consequence we show that these homomorphism spaces are one dimensional when q 6 1 we apply these results to complete the classification of the reducible specht modules for the hecke algebras of the symmetric groups when q 6 1 our methods can also be used to determine certain other pairs of specht modules between which there is a homomorphism in particular we describe the homomorphism space homh s n s for an arbitrary partition s although widely conjectured no q analogue of the full carter payne theorem is known in this paper we prove such an analogue in two important special cases namely when b a 1 or when 1 combinatorially this corresponds to moving an arbitrary number of nodes between adjacent rows or moving one node between an arbitrary number of rows it turns out that our proof has interesting implications we will turn our attention to the classification of the reducible specht modules for the algebras hf q sn when q 6 1 recent work see section 5 3 has resulted in the completion of this classification when q 1 combining our main result theorem 4 5 4 with previously published work we prove that a specht module is reducible if and only if it is e p reducible as defined in definition 5 1 we will also use our discussion of semistandard homomorphisms to obtain a description of the specht modules which contain a submodule isomorphic to the trivial module s n see

reducible specht modules abstract james and mathas conjecture a criterion for the specht module s for the symmetric group to be irreducible over a field of prime characteristic we extend a result of lyle to prove this conjecture in one direction our techniques are elementary

signed young modules and simple specht modules abstract by a result of hemmer every simple specht module of a finite symmetric group over a field of odd characteristic is a signed young module while specht modules are parametrized by partitions indecomposable signed young modules are parametrized by certain pairs of partitions the main result of this article establishes the signed young module labels of simple specht modules along the way we prove a number of results concerning indecomposable signed young modules that are of independent interest in particular we determine the label of the indecomposable signed young module obtained by tensoring a given indecomposable signed young module with the sign representation as consequences we obtain the green vertices green correspondents cohomological varieties and complexities of all simple specht modules and a class of simple modules of symmetric groups and extend the results of gill on periodic young modules to periodic indecomposable signed young modules

stochastic garch dynamics describing correlations between stocks the arch and garch processes have been successfully used for modelling price dynamics such as stock returns or foreign exchange rates analysing the long range correlations between stocks we propose a model based on the garch process which is able to describe the main characteristics of the stock price correlations including the mean variance probability density distribution and the noise spectrum

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

irreducibility of induced supermodules for general linear supergroups abstract in this note we determine when an induced supermodule h g 0 corresponding to a dominant integral highest weight of the general linear supergroup g g l m n is irreducible using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of weyl supermodules v this extends the result of kac 12 13 who proved that for ground fields of characteristic zero v is irreducible if and only if is typical

on the facial structure of the unit ball in the dual space of a jb triple it is shown that every proper weak closed face of the closed unit ball e 1 in the dual space of a jb triple e coincides with set of all elements in the unit sphere of e attaining their norm at a unique compact tripotent in e in particular every proper weak closed face of the closed unit ball e 1 is weak semi exposed this result provides an affirmative answer to a conjecture posed over 20 years ago

irreducible specht modules are signed young modules recently donkin defined signed young modules as a simultaneous generalization of young and twisted young modules for the symmetric group we show that in odd characteristic if a specht module s is irreducible then s is a signed young module thus the set of irreducible specht modules coincides with the set of irreducible signed young modules this provides evidence for our conjecture that the signed young modules are precisely the class of indecomposable self dual modules with specht filtrations the theorem is false in characteristic two

irreducible specht modules for hecke algebras of type a abstract let f be a field n a non negative integer a partition of n and s the corresponding specht module for the iwahori hecke algebra h f q s n james and mathas conjecture a necessary and sufficient condition on for s to be irreducible we prove the sufficiency of this condition in the case where f has infinite characteristic and also in the case where q 1