Celebratio Mathematica — Benkart

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G. Benkart and S. Witherspoon: “Restricted two-parameter quantum groups,” pp. 293–318 in Representations of finite dimensional algebras and related topics in Lie theory and geometry (15 July–10 August 2002, Toronto). Edited by V. Dlab and C. M. Ringel. Fields Institute Communications 40. American Mathematical Society (Providence, RI), 2004. MR 2057401 Zbl 1048.16020 incollection

Vlastimil B. Dlab	Related
Sarah J. Witherspoon	Related

G. Benkart and D. Moon: “Tensor product representations of Temperley–Lieb algebras and Chebyshev polynomials,” pp. 57–80 in Representations of algebras and related topics (15 July–10 August 2002, Toronto). Edited by R.-O. Buchweitz and H. Lenzing. Fields Institute Communications 45. American Mathematical Society (Providence, RI), 2005. To Professor Vlastimil Dlab with our best wishes on our seventieth birthday. MR 2146240 Zbl 1179.17009 incollection

The Brauer algebra \( B_k(n) \) determines the centralizer algebra of the action of the orthogonal group \( O_n \) on the \( k \)-fold tensor power \( V^{\otimes k} \) of its natural \( n \)-dimensional module \( V \). As a subalgebra of the Brauer algebra, the Temperley–Lieb alebra \( TL_k(n) \) inherits an action on \( V^{\otimes k} \). In this work, we investigate the centralizer algebra \( \mathcal{Z}_k(n) \) of the Temperley–Lieb algera on this tensor product space. We show that the dimesions of the irreducible \( \mathcal{Z}_k(n) \)-modules are related to vlaues of Chebyshev polynomials of the second kind. We determine the branching rule from \( B_k(n) \) to \( TL_k(n) \) using inverse Chebyshev relations.

Dong Ho Moon	Related
Vlastimil B. Dlab	Related