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New Expressions for Level-restricted Kostka Polynomials

In: Formal Power Series and Algebraic Combinatorics

Author

Listed:
  • Anne Schilling

    (MIT, Department of Mathematics)

  • Mark Shimozono

    (Virginia Tech, Department of Mathematics)

Abstract

We show that the bijection between tableaux and rigged configurations introduced by Kirillov and Reshetikhin is well-behaved with respect to level-restriction. hi particular we give an explicit characterization of the image of level-restricted tableaux under this bijection which yields new expressions for level-restricted Kostka polynomials. We conjecture that the bijection is also well-behaved with respect to skew shapes and give an explicit characterization of the image under the bijection. Type  branching functions can be expressed in terms of limits of level-restricted Kostka polynomials, thereby also yielding new expressions for these branching functions.

Suggested Citation

  • Anne Schilling & Mark Shimozono, 2000. "New Expressions for Level-restricted Kostka Polynomials," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 367-378, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_33
    DOI: 10.1007/978-3-662-04166-6_33
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