Symmetric functions and Springer representations
Representation Theory
2021-12-17 v3 Commutative Algebra
Combinatorics
Quantum Algebra
Abstract
The characters of the (total) Springer representations are identified with the Green functions by Kazhdan [Israel J. Math. {\bf 28} (1977)], and the latter are identified with Hall-Littlewood's -functions by Green [Trans. Amer. Math. Soc. (1955)]. In this paper, we present a purely algebraic proof that the (total) Springer representations of are -orthogonal to each other, and show that it is compatible with the natural categorification of the ring of symmetric functions.
Cite
@article{arxiv.2011.08374,
title = {Symmetric functions and Springer representations},
author = {Syu Kato},
journal= {arXiv preprint arXiv:2011.08374},
year = {2021}
}
Comments
26pp, v2: corrected an error in the proof of (old) Proposition 2.28, v3: streamlined the exposition, final version