Moscow-Petersburg seminar on low-dimensional mathematics
September 24, 2004
V.Fock
Cluster structure for Lie groups
The aim of the talk is to advertise the notion of the cluster structure with
the most widely known object --- simple Lie groups. The cluster approach
provides them with parameterization, giving especially simple explicit
expressions for many quantities, such as group multiplication, Gauss
decomposition, Drinfeld-Jimbo Poisson-Lie bracket, quantization of the space
of functions (without using $R$-matrix, positive structure, tropical limit
and others. One of the application of the cluster approach is an elementary
definition of the dual canonical basis of Lustig --- a certain
generalization of the Fourier transform for noncommutative groups.
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http://www.pdmi.ras.ru/~lowdimma