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Hall–Littlewood Vertex Operators and Generalized Kostka Polynomials

✍ Scribed by Mark Shimozono; Mike Zabrocki

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
182 KB
Volume
158
Category
Article
ISSN
0001-8708

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✦ Synopsis

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)_C)equivariant K-theory of the nullcone.

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