Search Results

OK, this is a very broad question so I'll be telegraphic. There is a sequence of increasingly detailed conjectures going by the name GL -- it's really a "program" (harmonic analysis of $\mathcal{D}$-m …

Well the first thing to say is to look at the very enthusiastic and world-encompassing papers of Cherednik himself on DAHA as the center of the mathematical world (say his 1998 ICM). I'll mention a c …

From the point of view of geometry, the crucial fact about $\rho$ is that the corresponding line bundle on the flag manifold is (upt to a sign) a (the) square-root of the canonical bundle (top exteri …

For context for Tom's answer, let me state the naive version of the conjecture, which has been around since around 1997 I think (due to Beilinson-Drinfeld). It calls for an equivalence of (dg) catego …

The dual Coxeter number comes up naturally as a normalization factor for invariant bilinear forms on the Lie algebra: according to Kac's book which you quote, $2h^{\vee}$ is the ratio between the Kill …

It might be worth pointing out a different motivation for Category O, namely the theory of Harish Chandra (g,K) modules. These are algebraic models for continuous representations of real reductive gro …

To elaborate on Kevin's excellent answer, one can account for the current absence of "higher loop" representation theory using physics. Namely, all of the representation theoretic structures you menti …

The videos from the LMS lectures and all of the GRASP videos are now available again from the links you gave (for download, not streaming). Many apologies for their long hiatus offline and many thanks …

There is an extensive math literature on related constructions. The key word is "chiral de Rham complex", introduced by Malikov, Schechtman and Vaintrob here and further developed in many many papers, …

The two are naturally dual lattices. The fundamental group of a torus $T$ can be canonically identified with the group (known as the cocharacter lattice) of $\it homomorphisms$ from the circle group t …

Local spaces:finite subschemes::Factorization spaces:finite subsets. A local space over X is a compatible collection of spaces over the Hilbert schemes of arbitrary numbers of points in X satisfying …

For Question 1 I agree with dhy that Namikawa's work is the relevant place to start, and from there the booming field of symplectic representation theory, which from one perspective is all about gener …

[Edited to reflect Reimundo's comment] The question addresses categorified versions of the Borel-Weil-Bott theorem (and more generally Beilinson-Bernstein localization), which states an equivalence b …

One natural generalization is the center of the group algebra (i.e., algebra of class functions - so in the abelian case you consider, just the group algebra itself). In the continuous case there are …

The de Rham space of a scheme is essentially never a scheme or algebraic space (unless I guess you're Spec of an Artin ring, in which case you'll get a discrete set of points). In particular this appl …