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Relations between generalised Gelfand-Tsetlin and Kazhdan-Lusztig bases of $S_n$

Ali Haidar, Oded Yacobi

Abstract

We prove that the Kazhdan-Lusztig basis of Specht modules is upper triangular with respect to all generalized Gelfand-Tsetlin bases constructed from any multiplicity-free tower of standard parabolic subgroups.

Relations between generalised Gelfand-Tsetlin and Kazhdan-Lusztig bases of $S_n$

Abstract

We prove that the Kazhdan-Lusztig basis of Specht modules is upper triangular with respect to all generalized Gelfand-Tsetlin bases constructed from any multiplicity-free tower of standard parabolic subgroups.

Paper Structure

This paper contains 8 sections, 9 theorems, 25 equations.

Table of Contents

  1. Introduction
  2. Background
  3. Generalised Gelfand-Tsetlin bases
  4. The main theorem
  5. Proof of Theorem \ref{['thm:main']}
  6. Case 1
  7. Case 2
  8. acknowledgements

Key Result

Theorem 2.1

BZ96Mathas96Stem96 Let $\lambda \vdash n$ and let $T \in \mathrm{SYT}(\lambda)$. Then $w_0\cdot c_T = \pm c_{\overline{T}}$, and the sign depends only on $\lambda$.

Theorems & Definitions (19)

  • Theorem 2.1
  • Proposition 2.2
  • Definition 3.1
  • Proposition 3.2
  • Lemma 3.3
  • proof
  • Definition 4.1
  • Theorem 4.2
  • Remark 4.4
  • Remark 4.5
  • ...and 9 more