3
votes
1answer
169 views

Spectral synthesis for central functions on locally compact groups

There is a large literature on harmonic analysis on locally compact group, that I am just beginning to discover. However I have not seen so far anything that emphasizes the central functions on $G$. A ...
9
votes
4answers
892 views

Coincidences amongst classifying spaces and Eilenberg Mac-Lane spaces

Given that $$\mathbb{R}P^{\infty} = B O(1) = K(\widehat{O(1)}, 1)$$ $$\mathbb{C} P^{\infty} = B U(1) = K( \widehat{U(1)}, 2)$$ is there any way to make sense of $$\mathbb{H}P^{\infty} = B Sp(1)$$ in a ...
2
votes
0answers
166 views

open orbits and invariant distributions

Suppose $G$ is a p-adic algebraic group, $P=MN$ a parabolic subgroup of $G$ with its Levi decomposition, $\sigma$ be a irreducible representation of $M$, we use $I(\sigma)$ to denote the unique ...
5
votes
1answer
621 views

Fiber functor of category of D-module on affine Grassmannian.

Geometric Satake correspondence allows us to construct Langlands dual group in a canonical way. In Mirkovic-Vilonen's paper, they prove that category of spherical perverse sheaves is an commutative ...