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q-Deformed character theory for infinite-dimensional symplectic and orthogonal groups

Cuenca, Cesar and Gorin, Vadim (2020) q-Deformed character theory for infinite-dimensional symplectic and orthogonal groups. Selecta Mathematica - New Series, 26 (3). Art. No. 40. ISSN 1022-1824.

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The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding finite-dimensional groups, as the rank tends to infinity. We solve a q-deformed version of the latter problem for orthogonal and symplectic groups, extending previously known results for the unitary group. The proof is based on novel determinantal and double-contour integral formulas for the q-specialized characters.

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Additional Information:© 2020 Springer Verlag. Published 12 June 2020. We would like to thank G. Olshanski for encouraging us to study whether the extension of [15] to orthogonal and symplectic groups is possible and for a number of fruitful discussions. V.G. was partially supported by the NSF Grant DMS-1664619, NSF Grant DMS-1949820, by the NEC Corporation Fund for Research in Computers and Communications, and by the Sloan Research Fellowship. The authors also thank the organizers of the Park City Mathematics Institute research program on Random Matrix Theory, where part of this work was carried out.
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Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:3
Classification Code:MSC: Primary 33D52; Secondary 60C05
Record Number:CaltechAUTHORS:20200702-070530970
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Official Citation:Cuenca, C., Gorin, V. q-Deformed character theory for infinite-dimensional symplectic and orthogonal groups. Sel. Math. New Ser. 26, 40 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104198
Deposited By: Tony Diaz
Deposited On:02 Jul 2020 15:18
Last Modified:02 Jul 2020 15:18

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