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The Irreducible Representations of the Hecke Category

โœ Scribed by Masashi Kosuda

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
442 KB
Volume
215
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

author thanks H. Mitsuhashi and T. Sugitani who read this paper and gave him useful advice. He also thanks N. Kawanaka, T. Kohno, and J. Murakami for their kind encouragement. When the w x author was writing the previous paper 8 with J. Murakami, he was informed by S. Okada of w x w x the existence of the paper 2 . In the paper 2 , they also constructed a complete set of irreducible representations of the algebra B n which corresponds to the case where q goes to k, l ลฝ n y1 . 1 in the algebra H C; q , q y q . He thanks S. Okada for the communication. Some of k, l ลฝ k, l k, l . the results in this paper for the specific case of the algebras H H โ‘€ , โ‘€ appear in the Ph.D. w x ลฝ ลฝ k, l k, l . . thesis of R. Leduc 9 . For the definition of H H โ‘€ , โ‘€ , see Section 6. Leduc considered ลฝ ลฝ . y1 . ลฝ ลฝ k, l k, l . . the algebra H C x, q , x, q y q the algebra H H โ‘€ , โ‘€ in this paper . In particular, k, l versions of the Theorems 0.1, 0.2, 6.6, and 6.7 appear there for this algebra. The formula for w x ลฝ . the weight s โฅ in 4.3 is also given in the paper as the values of the Markov trace on minimal idempotents. These facts were pointed out by the referee. The author also thanks him.

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