Status | Confirmed |
Seminar Series | SEM-LPTHE |
Subjects | cond-mat.stat-mech,hep-th,math-ph |
Date | Thursday 5 October 2017 |
Time | 11:00 |
Institute | LPTHE |
Seminar Room | Bibliothèque |
Speaker's Last Name | Zuber |
Speaker's First Name | Jean-Bernard |
Speaker's Email Address | |
Speaker's Institution | LPTHE |
Title | Horn's problem, from classical to quantum |
Abstract | Horn's (classical) problem deals with the following question: what can be said about the spectrum of eigenvalues of the sum C=A+B of two Hermitian matrices of given spectrum ? Curiously this problem is intimately related to the "quantum" problem : given two irreducible representations of SU(n), which irreps appear in their tensor product ? The support of the spectrum of C is well understood, after a long series of works from Weyl (1912) to Knutson and Tao (1999), and the classical problem is known to provide an asymptotic approach of the quantum one. Here I show how an explicit computation based on a well-known matrix integral enables one to determine the probability distribution of the eigenvalues of C, and sheds some new light on the relation between the classical and quantum problems. |
arXiv Preprint Number | |
Comments | |
Attachments |
To Generate a poster for this seminar : [ Postscript | PDF ]
|
[ English version ] |