Higher level affine Schur and Hecke algebras |
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| Authors: | Ruslan Maksimau Catharina Stroppel |
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| Institution: | 1. Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, 34095 Montpellier, France;2. Department of Mathematics, University of Bonn, 53115 Bonn, Germany;1. National Research University Higher School of Economics, Faculty of Computer Science, Pokrovsky Boulevard 11, Moscow, 109028, Russia;2. Instituto de Matemática y Física, Universidad de Talca, Casilla 721, Talca, Chile;3. Department of Mathematics and Mechanics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia;1. Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, United States of America;2. Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States of America |
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| Abstract: | We define a higher level version of the affine Hecke algebra and prove that, after completion, this algebra is isomorphic to a completion of Webster's tensor product algebra of type A. We then introduce a higher level version of the affine Schur algebra and establish, again after completion, an isomorphism with the quiver Schur algebra. An important observation is that the higher level affine Schur algebra surjects to the Dipper-James-Mathas cyclotomic q-Schur algebra. Moreover, we give nice diagrammatic presentations for all the algebras introduced in this paper. |
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| Keywords: | 20C08 20B30 18M30 |
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