2018/12/11 by Jun Hu, Hu, Jun, Yujiao Sun +1
Mathematics · #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1812.04231
openalex publication_date 2018/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (W,S) be a Coxeter system and ∗ an automorphism of W with order ≤ 2 and S∗=S. Lusztig and Vogan ([11], [14]) have introduced a u-deformed version Mu of Kottwitz's involution module over the Iwahori-Hecke algebra \mathscrHu(W) with Hecke parameter u2, where u is an indeterminate. Lusztig has proved that Mu is isomorphic to the left \mathscrHu(W)-submodule of \mathscrHu generated by X∅:=∑w^*=w∈ Wu-ℓ(w)Tw, where \mathscrHu is the vector space consisting of all formal (possibly infinite) sums ∑x∈ WcxTx (cx∈ℚ(u) for each x). He speculated that one can extend this by replacing u with any λ∈ ℂ∖\0,1,-1\. In this paper, we give a positive answer to his speculation for any λ∈ K∖\0,1,-1\ and any W, where K is an arbitrary ground field.