A new quantum analog of the Brauer algebra

Abstract

We introduce a new algebra B_l(z,q) depending on two nonzero complex parameters such that B_l(q^n,q) at q=1 coincides with the Brauer algebra B_l(n). We establish an analog of the Brauer-Schur-Weyl duality where the action of the new algebra commutes with the representation of the twisted deformation U'_q(o_n) of the enveloping algebra U(o_n) in the tensor power of the vector representation.

13 pages

References in corpus (1)

• q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

Cited by in corpus (7)

• Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
• (Quantum) twisted Yangians: symmetry, Baxterisation and centralizers
• Quantized enveloping superalgebra of type $P$
• Quantum supersymmetric pairs of basic types
• Cellular structure of $q$-Brauer algebras
• 2-Homogeneous bipartite distance-regular graphs and the quantum group $U_q^{\prime }({\mathfrak{so}}_6)$
• The disoriented skein and iquantum Brauer categories