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Download Algebraic and Analytic Methods in Representation Theory by Bent Orsted PDF

By Bent Orsted

This ebook is a compilation of a number of works from well-recognized figures within the box of illustration thought. The presentation of the subject is exclusive in delivering a number of various issues of view, which may still makethe publication very helpful to scholars and specialists alike. offers a number of diversified issues of view on key subject matters in illustration idea, from the world over recognized specialists within the box

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AP] H. H. Andersen and J. Paradowski, Fusion categories arising from semisimple Lie algebras, Comm. Math. Phys. 169 (1995), 563-588. [APW] H. H. Andersen, P. Polo, and K. Wen, Representations of quantum algebras, Invent. Math. 104 (1991), 1-59. [Bo] R. Bott, Homogeneous vector bundles, Ann. of Math. (2), 66 (1957), 203-248. [Cu] C. W. Curtis, Representations of Lie algebras of classical type with applications to linear groups, J. Math. Mech. 9 (1960), 307-326. [De] M, Demazure, A very simple proof of Bott's theorem, Invent.

Phys. 149 (1992), 149-159. [AJSI H. H. Andersen, J. C. Jantzen, and W. Soergel, Representations of quantum groups at a p-th root of unity and of semisimple groups in characteristic p: independence of p, Asterisque 220 (1994). [AP] H. H. Andersen and J. Paradowski, Fusion categories arising from semisimple Lie algebras, Comm. Math. Phys. 169 (1995), 563-588. [APW] H. H. Andersen, P. Polo, and K. Wen, Representations of quantum algebras, Invent. Math. 104 (1991), 1-59. [Bo] R. Bott, Homogeneous vector bundles, Ann.

Chapter 1 5 Modular Representations 19 R e p r e s e n t a t i o n s of SL2(k) In this section, we set G = SL2(k) and t U-{(0 0 tEk×}, 1 u 1) ~ E k}, t t- 1 t E k x ~1,E k It is then straightforward to check that G-BUU(0 \ 1 -1'~ B 0 / (disjoint union). Set V = k[X,Y], and let G act on V by b) a d c forall ( ac f(X,Y)- db ) E G, f ( X , Y ) f ( a X + cY, bX + dY), E k[X,Y]. Then V is a rational G-module. , where V~ = span k { x i Y j I i ÷ j = n}. 1), these formulas tell everything. In this case, X ( T ) = Z.

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