Generating functions for characters and weight multiplicities of irreducible 𝓈𝓁(4)-modules
- 10.1080/14029251.2018.1503436How to use a DOI?
- Calogero-Sutherland models; Generating functions; Lie algebra representation theory
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 (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.
- © 2018 The Authors. Published by Atlantis and Taylor & Francis
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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 -