English

Multiplicities, pictographs, and volumes

Mathematical Physics 2020-10-13 v1 Group Theory math.MP Representation Theory

Abstract

The present contribution is the written counterpart of a talk given in Yerevan at the SQS'2019 International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2019, 26 August - August 31, 2019). After a short presentation of various pictographs (O-blades, metric honeycombs) that one can use in order to calculate SU(n) multiplicities (Littlewood-Richardson coefficients, Kostka numbers), we briefly discuss the semi-classical limit of these multiplicities in relation with the Horn and Schur volume functions and with the so-called Rn-polynomials that enter the expression of volume functions. For n < 7 the decomposition of the Rn-polynomials on Lie group characters is already known, the case n=7 is obtained here.

Keywords

Cite

@article{arxiv.2003.00358,
  title  = {Multiplicities, pictographs, and volumes},
  author = {Robert Coquereaux},
  journal= {arXiv preprint arXiv:2003.00358},
  year   = {2020}
}

Comments

13 pages, 5 figures, to appear in the proceedings of the SQS'2019 International Workshop "Supersymmetries and Quantum Symmetries" held in Yerevan (26 August - August 31, 2019)