Local Systems and the Lusztig-vogan Bijection
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چکیده
منابع مشابه
On the Equivariant K -theory of the Nilpotent Cone in the General Linear Group
Let G be a simple complex algebraic group. Lusztig and Vogan have conjectured the existence of a natural bijection between the set of dominant integral weights of G, and the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit. This conjecture has been proved by Bezrukavnikov. In this paper, we develop combinatorial ...
متن کاملCorrections To: “on the Equivariant K -theory of the Nilpotent Cone in the General Linear Group”
In the paper [P. Achar, On the equivariant K-theory of the nilpotent cone in the general linear group, Represent. Theory 8 (2004), 180–211], the author gave a combinatorial algorithm for computing the Lusztig–Vogan bijection for GL(n,C). However, that paper failed to mention one easy case that may sometimes arise, making the description of the algorithm incomplete. This note fills in that gap.
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In this note we construct a “Kazhdan-Lusztig type” basis in equivariant K-theory of the nilpotent cone of a simple algebraic group G. This basis conjecturally is very close to the basis of this K-group consisting of irreducible bundles on nilpotent orbits. As a consequence we get a natural (conjectural) construction of Lusztig’s bijection between dominant weights and pairs {nilpotent orbit O, i...
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Let (W,S) be a Coxeter system and let w → w∗ be an involution of W which preserves the set of simple generators S. Lusztig and Vogan have recently shown that the set of twisted involutions (i.e., elements w ∈ W with w−1 = w∗) naturally generates a module of the Hecke algebra of (W,S) with two distinguished bases. The transition matrix between these bases defines a family of polynomials Pσ y,w w...
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In the context of the local Langlands philosopy for R, Adams, Barbasch and Vogan describe a bijection between the simple Harish-Chandra modules for a real reductive group G(R) and the space of “complete geometric parameters”—a space of equivariant local systems on a variety on which the Langlands-dual of G(R) acts. By a conjecture of Soergel, this bijection can be enhanced to an equivalence of ...
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