Bibliographical notes
1.1. For a detailed treatment of Grassmannians and Pl¨ ucker relations we ad-
dress the reader to [HdP] or [GrH].
1.2. The standard material about simple Lie algebras and groups can be found
in [Hu2] and [OV]. For a good introduction to Coxeter groups, including reduced
words for pairs of elements, Bruhat decompositions and Bruhat cells, see [Hu3].
Double Bruhat cells were introduced and studied in [FZ1], as well as generalized
minors and their twisted counterparts.
1.3. The bulk of the material reviewed in this section, including Drinfeld’s
theorem and Proposition 1.6, can be found in [ES] and [ReST]. For an introduction
to symplectic manifolds and Hamilton vector fields, see [A2]. The description of
the standard Poisson–Lie structure on a simple Lie group follows [HKKR] and
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