Combinatorial Invariance of Relative R-polynomials in the Hermitian Symmetric Case

W. Andrew Pruett

Combinatorial Invariance of Relative R-polynomials in the Hermitian Symmetric Case

Combinatorics 2009-12-01 v1 Representation Theory

Authors: W. Andrew Pruett

Abstract

We develop a marking system for an analog of Hasse diagrams of intervals $[u,v]$ with $u\leq v$ in a Hermitian symmetric pair $W/W_J$ , and use this to create a closed form algorithm for computing relative R-polynomials. The uniform nature of this algorithm allows us to show combinatorial invariance of relative Kazhdan-Lusztig polynomials in the Hermitian symmetric space setting.

Keywords

combinatorial invariance relative R-polynomials Kazhdan-Lusztig polynomials Hermitian symmetric pair Hasse diagram marking system closed form algorithm

Cite

@article{arxiv.0911.5694,
  title  = {Combinatorial Invariance of Relative R-polynomials in the Hermitian Symmetric Case},
  author = {W. Andrew Pruett},
  journal= {arXiv preprint arXiv:0911.5694},
  year   = {2009}
}

Comments

21 pages, 2 figures

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