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### Hypercube decompositions and combinatorial invariance for Kazhdan-Lusztig polynomials

**Algebra & Discrete Mathematics**

Speaker: | Christian Gaetz, UC Berkeley |

Location: | 1147 MSB |

Start time: | Fri, Oct 4 2024, 3:10PM |

Kazhdan-Lusztig polynomials are of foundational importance in geometric representation theory. Yet the Combinatorial Invariance Conjecture, due to Lusztig and to Dyer, suggests that they only depend on the combinatorics of Bruhat order. I'll describe joint work with Grant Barkley in which we adapt the hypercube decompositions introduced by Blundell-Buesing-Davies-Veličković-Williamson to prove this conjecture for Kazhdan-Lusztig R-polynomials in the case of elementary intervals in the symmetric group. This significantly generalizes the main previously known case of the conjecture, that of lower intervals.