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Register a new userIrreducible modules for pseudo-reductive groups
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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.
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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 $A_{n+1}^q$.
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