Séminaire Lotharingien de Combinatoire, 93B.23 (2025), 12 pp.
Gavin Hobbs, Tommy Parisi, Mark Skandera and Jiayuan Wang
A Generalization of Deodhar's Defect Statistic for Iwahori-Hecke Algebras of Type BC
Abstract.
Let H be the Iwahori-Hecke algebra corresponding to any Coxeter group.
Deodhar's {\em defect} statistic [{\em Geom.\;Dedicata} {\bf 36}, no.\,1 (1990)]
allows one to expand products of
simple Kazhdan-Lusztig basis elements of H in the natural basis of H.
Billey and Warrington [J. Algebraic Combin. 13, no. 2 (2001)]
provided a graphical interpretation of the type-A case of this formula.
Clearwater and the third author
[Ann. Comb. 25, no. 3 (2021)]
extended
the graphical type-A case
of this formula
to combinatorially expand
products of
Kazhdan-Lusztig basis elements
indexed by "smooth"
elements of the symmetric group.
We similarly extend the
type-BC case of
Deodhar's result to combinatorially expand
products of Kazhdan-Lusztig basis elements indexed by hyperoctahedral group elements which are ``simultaneously smooth" in types B and C.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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