Nilpotent Orbits in Representation Theory

By J. Jantzen. 2004

337 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0d388d534faf525dddb27083a00ba31850db337b

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In Algebra and Number Theory

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Citations in the corpus

Quantized symplectic actions and W -algebras (2007, methodology): “J1, J2 with their closures, we may assume that J1, J2 are closed.”
Nilpotent commuting varieties of reductive Lie algebras (2003, background): “4.14], it can be assumed that ereg = eα1 + ... +eαl where eαi are simple root vectors in g (the argument in [ 16 ] is based on [7, Prop.”
Closed Orbits and uniform S-instability in Geometric Invariant Theory (2009, background): “This optimality notion has had several applications, including to G-complete reducibility [1], [2], [4] and the theory of associated cocharacters for nilpotent elements of LieG [14], [26]; see [24, p.”
Component groups of unipotent centralizers in good characteristic (2002, methodology): “Moreover,CG(u) P . Proof. [ Jan , Prop. 5.9]”
Highest Weight Theory for Finite W-Algebras (2008, background): “q(u) = (1 +I)u) for u2 U(eg) and kerq = J n U(bg)0nch (resp.”
On symmetric invariants of centralisers in reductive Lie algebras (2006, methodology): “for i= d 1 +2,...,d 1 +d 2 + 2, degeF i > 3 for i= d 1 +d 2 +3,...,d 1 + d 2 +d 3 +3, and so on. Consequently, Pn i=1 deg eF i > Pk i=1 i(di+1). On the other hand, using the formula for dimgein [15] we obtain dimge= Xk i=1 (2i−1)(di+1) = 2 Xk i=1 i(di+1)− n; see also [5, p.398]. Inview of Theo”
Nilpotent orbits over ground fields of good characteristic (2002, methodology): “Pommerening’s proof eventually shows (after some case analysis) that one can associate to any nilpotent X ∈ g a collection of cocharacters of G with favorable properties; see [J04].”
Representations of Lie superalgebras in prime characteristic I (2008, background): “1 just as for semisimple Lie algebras in characteristic zero (compare with [9]).”
Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups (2011, background): “) We note that the proofs of the above results, as given in [15], do not depend upon case-by-case consideration of the list of nilpotent orbits.”
Commutative quotients of finite W-algebras (2008, background): “on the aﬃne variety Sk ∩Yχ. For d∈ N, deﬁne g(d) k := {x∈ gk| dim(gk)x = d}. When p≫ 0, the centraliser (gk)xcoincides with the Lie algebra of (Gk)x= ZG k (x) and dim(gk)x= dim(Gk)xfor all x∈ gk; see [19], for instance. Since the set g (d) k is quasi-aﬃne, it decomposes as a union of ﬁnitely many ir”
Affine braid group actions on derived categories of Springer resolutions (2011, methodology): “his subsection we prove some elementary facts about the coadjoint action of Gin g∗. If pis not too small, then g∗ is isomorphic to gas a G-module, and all the results we need are well known (see e.g. [J3]). However, these facts have to be checked directly (without using g) if we want to relax the as”