Abstract
Frenkel, Khovanov and Kirillov showed that the parabolic Kazhdan-Lusztig basis of Iwahori-Hecke algebra associated to can be obtained as the canonical basis of a weight subspace of , where is the vector representation of the quantum group . In this paper, a similar problem for the case of Ariki-Koike algebra is discussed. We construct a certain basis of , which is fixed by the involution and is closely related to the canonical basis of , by making use of the representation of on . In the case where , i.e., in the case of Iwahori-Hecke algebra of type , this gives a basis different from the Kazhdan-Lusztig basis of .
Citation
Kiyotaka Ohkura. Toshiaki Shoji. "On certain bases for Ariki-Koike algebras arising from canonical bases for ." SUT J. Math. 38 (2) 145 - 173, June 2002. https://doi.org/10.55937/sut/1057898725
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