Non-Levi Closed Conjugacy Classes of SP q (2n)

Abstract

We construct an explicit quantization of semi-simple conjugacy classes of the complex symplectic group SP (2n) with non-Levi isotropy subgroups through an operator realization on highest weight modules over the quantum group U q sp(2n) .Mathematics Subject Classifications: 81R50, 81R60, 17B37.

Quantum Exceptional Group G2 and its Semisimple Conjugacy Classes

“…It is sufficient to prove that ker df (t) = ker df 1 (t)∩ker df 2 (t) has the same dimension as O t , cf. [5], Prop. 2.1.…”

Non-Levi closed conjugacy classes of SO q(N)

“…annihilates e µ , f µ , h µ . As in [2], our comultiplication is opposite to the comultiplication used in [18].…”

“…We adopt certain conventions concerning representations of quantum groups, which are similar to [2]. We assume that they are free modules over C[[ ]] and their rank will be referred to as dimension.…”

“…It is determined by the following requirements: i) xu, y = x, uy for all x ∈M ⋆ λ , y ∈M λ , u ∈ U q (g), ii) v ⋆ λ is orthogonal to all vectors of weight lower than λ, iii) it is normalized to v ⋆ λ , v λ = 1. As in [2], we introduce a subspace of weights that we use for the parametrization of M K , the moduli space of conjugacy classes with fixed K. Define E i ∈ h * , i = 1, . .…”

Quantization of borderline Levi conjugacy classes of orthogonal groups

“…This work completes construction of quantum semisimple conjugacy classes of SO(N) and, generally, of all simple groups of the infinite series. Classes of our present concern have isotropy subgroups with a Cartesian factor SO(2) × SO(P ), where P is of the same parity as N. Due to the isomorphism GL(1) ≃ SO(2), they form a borderline between the Levi and non-Levi families, whose bulk cases have been processed in [1,2,3].…”