Braid-group approach to the derivation of universal matrices

DOI10.1088/0305-4470/29/18/031zbMATH Open0901.17011arXivq-alg/9712038OpenAlexW3104891752MaRDI QIDQ4393646

Feng Pan, Lianrong Dai

Publication date: 2 December 1998

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: A new method for deriving universal v{R} matrices from braid group representation is discussed. In this case, universal v{R} operators can be defined and expressed in terms of products of braid group generators. The advantage of this method is that matrix elements of v{R} are rank independent, and leaves multiplicity problem concerning coproducts of the corresponding quantum groups untouched. As examples, v{R} matrix elements of $[1]imes[1]$, $[2]imes[2]$, $[1^2]imes[1^2]$, and $[21]imes[21]$ with multiplicity two for $A_n$, and $[1]imes[1]$ for $B_n$, $C_n$, and $D_n$ type quantum groups, which are related to Hecke algebra and Birman-Wenzl algebra, respectively, are derived by using this method.

Full work available at URL: https://arxiv.org/abs/q-alg/9712038

zbMATH Keywords

quantum groupsBirman-Wenzl algebraHecke algebrabraid-group representationuniversal \(\check R\) matrices

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Braid groups; Artin groups (20F36) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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