Chevalley restriction theorem for vector-valued functions on quantum groups

TY - JOUR

T1 - Chevalley restriction theorem for vector-valued functions on quantum groups

AU - Balagovic, Martina

PY - 2011/9/8

Y1 - 2011/9/8

N2 - We generalize Chevalley's theorem about restriction of \mathfrak{g}-invariant polynomial functions \mathfrak{g}->C to W-invariant functions on the Cartan \mathfrak{h}->C. We consider the case when \mathfrak{g} is replaced by a quantum group and the target space of the polynomial maps is replaced by a finite dimensional representation V of this quantum group. We prove that the restriction map Res:(O_q(G)\otimes V)^{U_q(\mathfrak{g})}-> O(H)\otimes V is injective and describe the image.

AB - We generalize Chevalley's theorem about restriction of \mathfrak{g}-invariant polynomial functions \mathfrak{g}->C to W-invariant functions on the Cartan \mathfrak{h}->C. We consider the case when \mathfrak{g} is replaced by a quantum group and the target space of the polynomial maps is replaced by a finite dimensional representation V of this quantum group. We prove that the restriction map Res:(O_q(G)\otimes V)^{U_q(\mathfrak{g})}-> O(H)\otimes V is injective and describe the image.

U2 - 10.1090/S1088-4165-2011-00408-8

DO - 10.1090/S1088-4165-2011-00408-8

M3 - Article

SN - 1088-4165

VL - 15

SP - 617

EP - 645

JO - Representation Theory

JF - Representation Theory

ER -