A generalization of Deodhar's defect statistic for Iwahori--Hecke algebras of type $BC$
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912449176797184 |
|---|---|
| author | Hobbs, Gavin Parisi, Tommy Skandera, Mark Wang, Jiayuan |
| author_facet | Hobbs, Gavin Parisi, Tommy Skandera, Mark Wang, Jiayuan |
| contents | Let $H$ be the Iwahori--Hecke algebra corresponding to any Coxeter group. Deodhar's defect statistic [Geom. Dedicata 36, (1990) pp.95--119] allows one to expand products of simple Kazhdan--Lusztig basis elements of $H$ in the natural basis of $H$. Clearwater and the third author gave a type-$A$ extension [Ann. Comb. 25, no. 3 (2021) pp.757--787] of this formula which combinatorially describes the natural expansion of products of Kazhdan--Lusztig basis elements indexed by smooth elements of the symmetric group. We similarly give a type-$BC$ extension of Deodhar's result which combinatorially describes the natural expansion of Kazhdan--Lusztig basis elements indexed by hyperoctahedral group elements which are simultaneously smooth in types $B$ and $C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalization of Deodhar's defect statistic for Iwahori--Hecke algebras of type $BC$ Hobbs, Gavin Parisi, Tommy Skandera, Mark Wang, Jiayuan Combinatorics Representation Theory 05E10, 20C08 Let $H$ be the Iwahori--Hecke algebra corresponding to any Coxeter group. Deodhar's defect statistic [Geom. Dedicata 36, (1990) pp.95--119] allows one to expand products of simple Kazhdan--Lusztig basis elements of $H$ in the natural basis of $H$. Clearwater and the third author gave a type-$A$ extension [Ann. Comb. 25, no. 3 (2021) pp.757--787] of this formula which combinatorially describes the natural expansion of products of Kazhdan--Lusztig basis elements indexed by smooth elements of the symmetric group. We similarly give a type-$BC$ extension of Deodhar's result which combinatorially describes the natural expansion of Kazhdan--Lusztig basis elements indexed by hyperoctahedral group elements which are simultaneously smooth in types $B$ and $C$. |
| title | A generalization of Deodhar's defect statistic for Iwahori--Hecke algebras of type $BC$ |
| topic | Combinatorics Representation Theory 05E10, 20C08 |
| url | https://arxiv.org/abs/2506.20099 |