On modular double of semisimple quantum groups

2018/11/27 by Sultanich, Pavel
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1811.10934

Abstract

In this note we propose a construction of the Hopf algebra of a complex analog of devided powers of the Weyl generators of a semisimple simply-laced quantum group. Here we consider the generators as positive, self-adjoint operators. In particular, we generalize the Lusztig relations on the usual divided powers of generators of a quantum group to the case of complex devided powers of generators. These relations, some of which were known present the complete set of defining relations. As a by-product result, the pure algebraic definition of the Faddeev modular double in the case of semisimple simply-laced quantum groups is formulated. Finally, we introduce an infinite dimension version of the Gelfand-Zetlin finite-dimensional representation of the modular double M_q,q(\mathfrakgl(N)).

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