By Henning Haahr Andersen (auth.), Akihiko Gyoja, Hiraku Nakajima, Ken-ichi Shinoda, Toshiaki Shoji, Toshiyuki Tanisaki (eds.)

ISBN-10: 0817646965

ISBN-13: 9780817646967

This quantity includes invited articles by way of top-notch specialists who specialize in such issues as: modular representations of algebraic teams, representations of quantum teams and crystal bases, representations of affine Lie algebras, representations of affine Hecke algebras, modular or usual representations of finite reductive teams, and representations of advanced mirrored image teams and linked Hecke algebras.

*Representation concept of Algebraic teams and Quantum Groups* is meant for graduate scholars and researchers in illustration thought, staff thought, algebraic geometry, quantum concept and math physics.

Contributors:

H. H. Andersen, S. Ariki, C. Bonnafé, J. Chuang, J. Du, M. Finkelberg, Q. Fu, M. Geck, V. Ginzburg, A. Hida, L. Iancu, N. Jacon, T. Lam, G.I. Lehrer, G. Lusztig, H. Miyachi, S. Naito, H. Nakajima, T. Nakashima, D. Sagaki, Y. Saito, M. Shiota, J. Xiao, F. Xu, R. B. Zhang

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**Sample text**

Assume that Lusztig’s conjectures (P1)–(P15) in [30, Sect. 2] hold for H. Assume also that H is normalized and integral. 10], we conclude that the sets L ;k and R ;k are precisely the left cells and the right cells of W , respectively. Now let W D Wn be the Coxeter group of type Bn as in Sect. 1; let Hn be the associated Iwahori–Hecke algebra with respect to the weight function L D La;b where a; b > 0. 3. n integral and normalized. 1/ag. Then Hn is Proof. The fact that Hn is normalized follows from the explicit description of a.

2 shows that there is a standard bitableau t such that if the residue sequence of t appears as the residue sequence of a standard bitableau of shape , then . Suppose that the residue sequence of t is the residue sequence of a standard bitableau of shape G . As G implies , we cannot have , a contradiction. Hence is restricted. 2 Remarks We conclude the chapter with two remarks. 4. In the language of the Fock space theory, the proof of the fact that restricted implies Kleshchev goes as follows. The proof in the introduction is the same proof, but it was explained in a different manner.

1/ , for k k or > j , and It is clear that if C , then . sl e /-module structure which is suitable for the Dipper–James– Murphy’s Specht module theory. 2. Let D. 2/ ; / be Kleshchev and let i1 ; : : : ; i1 ; : : : ; ip ; : : : ; ip „ ƒ‚ … „ ƒ‚ … a1 times ap times be an optimal sequence of . v/ ; , in the deformed Fock space. 30 S. Ariki and N. Jacon Proof. First note that the coefficient of is one because each admissible sequence of ij -nodes is a sequence of normal ij -nodes. Now the proposition is proved by induction on p.