Composition Kostka functions

Knop F (2007)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 2007

Publisher: Narosa Publishing House

Edited Volumes: Algebraic Groups and Homogeneous Spaces

Series: Tata Institute of Fundamental Research - Mumbai Studies in Mathematics

City/Town: New Delhi

Pages Range: 321-352

Abstract

Macdonald defined two-parameter Kostka functions K_λμ(q,t) where λ, μ are partitions. The main purpose of this paper is to extend his definition to include all compositions as indices. Following Macdonald, we conjecture that also these more general Kostka functions are polynomials in q and t^½ with non-negative integers as coefficients. If q=0 then our Kostka functions are Kazhdan-Lusztig polynomials of a special type. Therefore, our positivity conjecture combines Macdonald positivity and Kazhdan-Lusztig positivity and hints towards a connection between Macdonald and Kazhdan-Lusztig theory.

Authors with CRIS profile

Friedrich Knop Lehrstuhl für Mathematik (Algebra und Geometrie)

How to cite

APA:

Knop, F. (2007). Composition Kostka functions. In Vikram B. Mehta (Eds.), Algebraic Groups and Homogeneous Spaces. (pp. 321-352). New Delhi: Narosa Publishing House.

MLA:

Knop, Friedrich. "Composition Kostka functions." Algebraic Groups and Homogeneous Spaces. Ed. Vikram B. Mehta, New Delhi: Narosa Publishing House, 2007. 321-352.

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