Quantization of borderline Levi conjugacy classes of orthogonal groups

Abstract

We construct equivariant quantization of a special family of Levi conjugacy classes of the complex orthogonal group $SO(N)$, whose stabilizer contains a Cartesian factor $SO(2)\times SO(P)$, $1\leqslant P<N$, $P\equiv N \mod 2$.Comment: 23 pages, no figure

Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices

“…To end, let us mention that important motivation for this paper, in particular with respect to the use of the reflection equation, can be found in [85,86,80,53] and the work of Mudrov and collaborators [27][28][29][30][71][72][73]3,74,75,2,4]. We also mention that in a more restricted setting, constructions closely related to the ones in this paper were performed in [15].…”

Quantum Exceptional Group G2 and its Semisimple Conjugacy Classes

“…We select the subset T k reg ∈ T k of regular points, whose minimal polynomial in the basic representation has maximal degree. The complementary subset in T k is denoted by T k bord and called borderline, following [4]. Such points are present only for k = h and k = k l .…”

Representations of Quantum Conjugacy Classes of Orthosymplectic Groups

“…For the symplectic group, it is SP (2m) × SP (2p), where m, p 1. the isotropy subgroup stays within the Levi type. We distinguished such conjugacy classes as borderline Levi because they share some properties of both types, [5].…”

“…This paper is a sequel of a series of works on quantization of semisimple conjugacy classes of a non-exceptional simple Poisson group G, [1]- [5]. It is done in the spirit of [6] devoted to G = SL(n) and can be viewed as a uniform approach to quantization that includes the results of [1]- [5] as a special case.…”