TY - JOUR
T1 - Asymptotic Hecke Algebras and Lusztig-Vogan Bijection via Affine Matrix-Ball Construction
AU - Kim, Dongkwan
AU - Pylyavskyy, Pavlo
N1 - Publisher Copyright:
© 2023 The Author(s).
PY - 2023/9/1
Y1 - 2023/9/1
N2 - The affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of the Robinson-Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished involution in each Kazhdan-Lusztig cell of an affine symmetric group. We then use AMBC to give the 1st known canonical presentation for the asymptotic Hecke algebras of extended affine symmetric groups. As an application, we show that AMBC gives a conceptual way to compute the Lusztig-Vogan bijection. For the latter, we build upon prior works of Achar and Rush.
AB - The affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of the Robinson-Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished involution in each Kazhdan-Lusztig cell of an affine symmetric group. We then use AMBC to give the 1st known canonical presentation for the asymptotic Hecke algebras of extended affine symmetric groups. As an application, we show that AMBC gives a conceptual way to compute the Lusztig-Vogan bijection. For the latter, we build upon prior works of Achar and Rush.
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U2 - 10.1093/imrn/rnab191
DO - 10.1093/imrn/rnab191
M3 - Article
AN - SCOPUS:85174243865
SN - 1073-7928
VL - 2023
SP - 16051
EP - 16103
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 18
ER -