Some quantum analogues of solvable Lie groups

C. De Concini; C. Procesi; Victor G. Kac

Some quantum analogues of solvable Lie groups

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arxiv hep-th/9308138 v1 pith:LMJWF6QW submitted 1993-08-27 hep-th math.QA

C. De Concini , Victor G. Kac , C. Procesi This is my paper · ORCID

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In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras of twisted polynomials with a derivation, an object which has often appeared in the general theory of non-commutative rings. In particular, we find maximal dimensions of their irreducible representations. Our results confirm the validity of the general philosophy that the representation theory is intimately connected to the Poisson geometry.

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For every finite type quantum symmetric pair, the braid group action and a PBW basis descend to the DCKP-type integral form and, via semiclassical limits, yield Poisson automorphisms and explicit Poisson brackets on t...

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