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A geometric setting for the quantum deformation of \(\mathrm{GL}_n\). (English) Zbl 0713.17012

For the quantum deformation of \(\mathrm{GL}_n\) a realization is given not in terms of generators and relations which, according to Drinfel’d, “do not give much to heart or imagination” but in geometric terms of relative positions of pairs of flags in an infinite dimensional space. This infinite case is approximated by finite-dimensional ones via a nontrivial limiting procedure.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
16T20 Ring-theoretic aspects of quantum groups
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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References:

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