142 research outputs found
Hall-Littlewood vertex operators and generalized Kostka polynomials
A family of vertex operators that generalizes those given by Jing for the
Hall-Littlewood symmetric functions is presented. These operators produce
symmetric functions related to the Poincare polynomials referred to as
generalized Kostka polynomials in the same way that Jing's operator produces
symmetric functions related to Kostka-Foulkes polynomials. These operators are
then used to derive commutation relations and new relations involving the
generalized Kostka coefficients. Such relations may be interpreted as
identities in the (GL(n) x C^*)-equivariant K-theory of the nullcone.Comment: 17 page
Lusztig's q-analogue of weight multiplicity and one-dimensional sums for affine root systems
In this paper we complete the proof of the X=K conjecture, that for every
family of nonexceptional affine algebras, the graded multiplicities of tensor
products of symmetric power Kirillov-Reshetikhin modules known as
one-dimensional sums, have a large rank stable limit X that has a simple
expression (called the K-polynomial) as nonnegative integer combination of
Kostka-Foulkes polynomials. We consider a subfamily of Lusztig's q-analogues of
weight multiplicity which we call stable KL polynomials and denote by KL. We
give a type-independent proof that K=KL. This proves that X=KL: the family of
stable one-dimensional sums coincides with family of stable KL polynomials. Our
result generalizes the theorem of Nakayashiki and Yamada which establishes the
above equality in the case of one-dimensional sums of affine type A and the
Lusztig q-analogue of type A, where both are Kostka-Foulkes polynomials.Comment: 28 pages; incorrect section 3.4 replace
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