Journal of Nonlinear Mathematical Physics

Volume 25, Issue 4, July 2018, Pages 618 - 632

Generating functions for characters and weight multiplicities of irreducible 𝓈𝓁(4)-modules

Authors
José Ferńandez Núñez
Departamento de Física, Facultad de Ciencias, Universidad de Oviedo, 33007-Oviedo, Spain,nonius@uniovi.es
Wifredo García Fuertes
Departamento de Física, Facultad de Ciencias, Universidad de Oviedo, 33007-Oviedo, Spain,wifredo@uniovi.es
Askold M. Perelomov
Institute for Theoretical and Experimental Physics, Moscow, Russia,aperelomo@gmail.com
Received 22 January 2018, Accepted 14 May 2018, Available Online 6 January 2021.
DOI
10.1080/14029251.2018.1503436How to use a DOI?
Keywords
Calogero-Sutherland models; Generating functions; Lie algebra representation theory
Abstract

Generating functions for the characters of the irreducible representations of simple Lie algebras are rational functions where both the numerator and denominator can be expressed as polynomials in the characters corresponding to the fundamental weights. They encode much information on the representation theory of the algebra, but their explicit expressions are in general very complicated. In fact, it seems that rank three is the highest rank tractable. In this paper, we use a method based on the quantum Calogero-Sutherland model to compute the full generating function for the characters of irreducible modules over the complex Lie algebra 𝔰𝔩 (4), and exploit this result to obtain also generating functions giving the multiplicities of some low order weights in all representations. We have applied the same method to compute the generating function for the characters of the modules the other rank three simple Lie algebras, but in these cases the full expressions are very long and appear only in the arXiv version of the paper (arXiv:1705.03711 [math-ph]). Nevertheless, when the generating functions are limited to some particular subsets of characters, the results are quite simple and we present them here.

Copyright
© 2018 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
25 - 4
Pages
618 - 632
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2018.1503436How to use a DOI?
Copyright
© 2018 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - José Ferńandez Núñez
AU  - Wifredo García Fuertes
AU  - Askold M. Perelomov
PY  - 2021
DA  - 2021/01/06
TI  - Generating functions for characters and weight multiplicities of irreducible 𝓈𝓁(4)-modules
JO  - Journal of Nonlinear Mathematical Physics
SP  - 618
EP  - 632
VL  - 25
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1503436
DO  - 10.1080/14029251.2018.1503436
ID  - FerńandezNúñez2021
ER  -