Twisted geometric Satake equivalence via gerbes on the factorizable grassmannian
نویسندگان
چکیده
منابع مشابه
Twisted Geometric Satake Equivalence
Let k be an algebraically closed field and O = k[[t]] ⊂ F = k((t)). For an almost simple algebraic group G we classify central extensions 1 → Gm → E → G(F) → 1, any such extension splits canonically over G(O). Fix a positive integer N and a primitive character ζ : μN (k) → Q ∗ l (under some assumption on the characteristic of k). Consider the category of G(O)biinvariant perverse sheaves on E wi...
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Theorem 1. The convolution ∗ admits a commutativity constraint making Sph into a rigid tensor category. There exists a faithful, exact tensor “fiber” functor Sat : Sph → Vect inducing an equivalence (modulo a sign in the commutativity constraint) of Sph with Rep(G) as tensor categories, where G is the Langlands dual group of the reductive group G, whose weights are the coweights of G and vice v...
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For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...
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This paper begins a series studying D-modules on the Feigin-Frenkel semi-infinite flag variety from the perspective of the Beilinson-Drinfeld factorization (or chiral) theory. Here we calculate Whittaker-twisted cohomology groups of Zastava spaces, which are certain finite-dimensional subvarieties of the affine Grassmannian. We show that such cohomology groups realize the nilradical of a Borel ...
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The twisted Drinfeld double (or quasi-quantum double) of a finite group with a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid is the loop (or inertia) groupoid of the original group and the twisting is shown geometrically to be the loop transgression of the 3-cocycle. The twisted representation theory of finite groupoids is developed and used to derive properties ...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2012
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-2012-00420-4