TY - JOUR
T1 - BMW Algebra, quantized coordinate algebra and type C schur–weyl duality
AU - Hu, Jun
PY - 2011/1/10
Y1 - 2011/1/10
N2 - We prove an integral version of the Schur–Weyl duality between the specialized Birman–Murakami–Wenzl algebra Bn(−q2m+1, q) and the quantum algebra associated to the symplectic Lie algebra (formula presented)2m. In particular, we deduce that this Schur–Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang in the symplectic case. As a byproduct, we show that, as a ℤ[q, q−1]-algebra, the quantized coordinate algebra defined by Kashiwara (which he denoted by Aℤq (g)) is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev–Reshetikhin–Takhtajan construction.
AB - We prove an integral version of the Schur–Weyl duality between the specialized Birman–Murakami–Wenzl algebra Bn(−q2m+1, q) and the quantum algebra associated to the symplectic Lie algebra (formula presented)2m. In particular, we deduce that this Schur–Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang in the symplectic case. As a byproduct, we show that, as a ℤ[q, q−1]-algebra, the quantized coordinate algebra defined by Kashiwara (which he denoted by Aℤq (g)) is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev–Reshetikhin–Takhtajan construction.
KW - Birman–Murakami–Wenzl algebra
KW - Canonical bases
KW - Modified quantized enveloping algebra
UR - https://www.scopus.com/pages/publications/81555209875
U2 - 10.1090/S1088-4165-2011-00369-1
DO - 10.1090/S1088-4165-2011-00369-1
M3 - Article
AN - SCOPUS:81555209875
SN - 1088-4165
VL - 15
JO - Representation Theory
JF - Representation Theory
IS - 1
ER -