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June 2002 On certain bases for Ariki-Koike algebras arising from canonical bases for Uv(slm)
Kiyotaka Ohkura, Toshiaki Shoji
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SUT J. Math. 38(2): 145-173 (June 2002). DOI: 10.55937/sut/1057898725

Abstract

Frenkel, Khovanov and Kirillov showed that the parabolic Kazhdan-Lusztig basis of Iwahori-Hecke algebra associated to Sn can be obtained as the canonical basis of a weight subspace of Vn, where V is the vector representation of the quantum group Uv(slm). In this paper, a similar problem for the case of Ariki-Koike algebra n,r is discussed. We construct a certain basis of n,r, which is fixed by the involution and is closely related to the canonical basis of Vn, by making use of the representation of n,r on Vn. In the case where r = 2, i.e., in the case of Iwahori-Hecke algebra of type Bn, this gives a basis different from the Kazhdan-Lusztig basis of n,r.

Citation

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Kiyotaka Ohkura. Toshiaki Shoji. "On certain bases for Ariki-Koike algebras arising from canonical bases for Uv(slm)." SUT J. Math. 38 (2) 145 - 173, June 2002. https://doi.org/10.55937/sut/1057898725

Information

Received: 30 July 2002; Published: June 2002
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1057898725

Subjects:
Primary: 16G99 , 17B37

Keywords: Ariki-Koike algebra , canonical basis , Kazhdan-Lusztig basis , quantum group

Rights: Copyright © 2002 Tokyo University of Science

Vol.38 • No. 2 • June 2002
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