Titlebook: Representations of Reductive Groups; In Honor of the 60th Monica Nevins,Peter E. Trapa Book 2015 Springer International Publishing Switzerl

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Parameters for twisted representations,ig–Vogan polynomials for .. These were defined and studied by Lusztig and Vogan in [10]. In order to carry out the computation, we introduce new class of . parameters, and study the Hecke algebra action in the resulting basis.

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The smooth loci of spiral Schubert varieties of type ,,ocus in terms of the action of the Weyl group on .; using this result, we identify the maximal singular points of these varieties. We make key use of the results of [7] relating the Bruhat order to the Weyl group action on ..

Recess

,On the Gelfand–Kirillov dimension of a discrete series representation,dels for minimal parabolic subgroups are the “l(fā)argest” (a more precise result in the quasi-split case is due to Kostant). We also show that if . is quaternionic and not of type A or C, then the quaternionic discrete series is the “smallest”.

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0743-1643 depth and breadth of Vogan‘s influence on representation the.Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups.? His groundbreaking ideas have lead to deep advances in the theory of real and .p.-adic groups, and have forged lasting

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Book 2015 lead to deep advances in the theory of real and .p.-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics..Representations of Reductive Groups. is an outgrowth of the conference of the same name, dedic

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Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits,our earlier paper “Arithmetic invariant theory”, we provide necessary and sufficient conditions for a rational element of . to lie in the image of ., assuming that generic stabilizers are abelian. We illustrate the various scenarios that can occur with some recent examples of arithmetic interest.

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