TY - JOUR

T1 - The centralizer algebra of the diagonal action of the group GLn (ℂ) in a mixed tensor space

AU - Nikitin, P. P.

PY - 2007/3/1

Y1 - 2007/3/1

N2 - We consider the walled Brauer algebra Brk,l(n) introduced by V. Turaev and K. Koike. We prove that it is a subalgebra of the Brauer algebra and that it is isomorphic, for sufficiently large n ∈ ℕ, to the centralizer algebra of the diagonal action of the group GLn(ℂ) in a mixed tensor space. We also give the presentation of the algebra Br k,l(n) by generators and relations. For a generic value of the parameter, the algebra is semisimple, and in this case we describe the Bratteli diagram for this family of algebras and give realizations for the irreducible representations. We also give a new, more natural proof of the formulas for the characters of the walled Brauer algebras. Bibliography: 29 titles.

AB - We consider the walled Brauer algebra Brk,l(n) introduced by V. Turaev and K. Koike. We prove that it is a subalgebra of the Brauer algebra and that it is isomorphic, for sufficiently large n ∈ ℕ, to the centralizer algebra of the diagonal action of the group GLn(ℂ) in a mixed tensor space. We also give the presentation of the algebra Br k,l(n) by generators and relations. For a generic value of the parameter, the algebra is semisimple, and in this case we describe the Bratteli diagram for this family of algebras and give realizations for the irreducible representations. We also give a new, more natural proof of the formulas for the characters of the walled Brauer algebras. Bibliography: 29 titles.

UR - http://www.scopus.com/inward/record.url?scp=33846847965&partnerID=8YFLogxK

U2 - 10.1007/s10958-007-0053-1

DO - 10.1007/s10958-007-0053-1

M3 - Article

AN - SCOPUS:33846847965

VL - 141

SP - 1479

EP - 1493

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -