Representations of classical Lie groups and quantized free convolution
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Author(s)
Bufetov, Alexey
Gorin, Vadim
Date Issued
March 2015
Journal
Geometric and Functional Analysis
Publisher
Springer Basel
Citation
Bufetov, Alexey, and Vadim Gorin. “Representations of Classical Lie Groups and Quantized Free Convolution.” Geometric and Functional Analysis 25, no. 3 (March 6, 2015): 763–814.
Version
Author's final manuscript
Abstract
We study the decompositions into irreducible components of tensor products and restrictions of irreducible representations for all series of classical Lie groups as the rank of the group goes to infinity. We prove the Law of Large Numbers for the random counting measures describing the decomposition. This leads to two operations on measures which are deformations of the notions of the free convolution and the free projection. We further prove that if one replaces counting measures with others coming from the work of Perelomov and Popov on the higher order Casimir operators for classical groups, then the operations on the measures turn into the free convolution and projection themselves. We also explain the relation between our results and limit shape theorems for uniformly random lozenge tilings with and without axial symmetry.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00039-015-0323-x
