Specht Filtrations for Hecke Algebras of Type A |
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Authors: | Hemmer David J; Nakano Daniel K |
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Institution: | Department of Mathematics, University of Toledo 2801 W. Bancroft, Toledo, OH 43606, USA, david.hemmer{at}utoledo.edu
Department of Mathematics, University of Georgia Athens, GA 30602, USA, nakano{at}math.uga.edu |
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Abstract: | Let Hq(d) be the IwahoriHecke algebra of the symmetricgroup, where q is a primitive 1th root of unity. Using resultsfrom the cohomology of quantum groups and recent results aboutthe Schur functor and adjoint Schur functor, it is proved that,contrary to expectations, for l 4 the multiplicities in a Spechtor dual Specht module filtration of an Hq(d)-module are welldefined. A cohomological criterion is given for when an Hq(d)-modulehas such a filtration. Finally, these results are used to givea new construction of Young modules that is analogous to theDonkinRingel construction of tilting modules. As a corollary,certain decomposition numbers can be equated with extensionsbetween Specht modules. Setting q = 1, results are obtainedfor the symmetric group in characteristic p 5. These resultsare false in general for p = 2 or 3. |
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