SUT J. Math. 38 (2), 145-173, (June 2002) DOI: 10.55937/sut/1057898725
Kiyotaka Ohkura, Toshiaki Shoji
KEYWORDS: Ariki-Koike algebra, quantum group, canonical basis, Kazhdan-Lusztig basis, 17B37, 16G99
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 .