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Register a new userThe Duals of the 2-Modular Irreducible Modules of the Alternating Groups
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John Murray
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We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.
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We determine the quadratic type of the 2-modular principal indecomposable modules of the double covers of alternating groups.
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete description of the rank one case.
We give a classification of all irreducible completely pointed $U_q(mathfrak{sl}_{n+1})$ modules over a characteristic zero field in which $q$ is not a root of unity. This generalizes the classification result of Benkart, Britten and Lemire in the non quantum case. We also show that any infinite-dimensional irreducible completely pointed $U_q(mathfrak{sl}_{n+1})$ can be obtained from some irreducible completely pointed module over the quantized Weyl algebra $A_{n+1}^q$.
Answering a question of I. M. Isaacs, we show that the largest degree of irreducible complex representations of any finite non-abelian simple group can be bounded in terms of the smaller degrees. We also study the asymptotic behavior of this largest degree for finite groups of Lie type. Moreover, we show that for groups of Lie type, the Steinberg character has largest degree among all unipotent characters.
In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $Omega(lambda,alpha,h)$ defined in cite{CG}, with irreducible highest weight modules $V(theta,h)$ or with irreducible Virasoro modules Ind$_{theta}(N)$ defined in cite{MZ2}. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for two of them to be isomorphic. These modules are not isomorphic to any other known irreducible Virasoro modules.
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