Kirillov polynomials for the exceptional Lie algebra $\mathfrak g_2$
Representation Theory
2025-02-11 v1
Abstract
As part of the development of the orbit method, Kirillov has counted the number of strictly upper triangular matrices with coefficients in a finite field of elements and fixed Jordan type. One obtains polynomials with respect to with many interesting properties and close relation to type A representation theory. In the present work we develop the corresponding theory for the exceptional Lie algebra . In particular, we show that the leading coefficient can be expressed in terms of the Springer correspondence.
Keywords
Cite
@article{arxiv.2502.06718,
title = {Kirillov polynomials for the exceptional Lie algebra $\mathfrak g_2$},
author = {Martin T. Luu},
journal= {arXiv preprint arXiv:2502.06718},
year = {2025}
}