100 research outputs found
Difference Equations Compatible with Trigonometric KZ Differential Equations
The trigonometric KZ equations associated with a Lie algebra \g depend on a
parameter \lambda\in\h where \h\subset\g is the Cartan subalgebra. We
suggest a system of dynamical difference equations with respect to
compatible with the KZ equations. The dynamical equations are constructed in
terms of intertwining operators of \g-modules.Comment: 23 pages, AmsTeX, third version, some misprints were correcte
Selberg Type Integrals Associated with
We present several formulae for the Selberg type integrals associated with
the Lie algebra .Comment: Errata added; 13 pages, amstex.tex 2.2 and amssym.tex require
Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)
We consider a tensor product V(b)= \otimes_{i=1}^n\C^N(b_i) of the Yangian
evaluation vector representations. We consider the action of the
commutative Bethe subalgebra on a -weight subspace
of weight . Here the Bethe algebra depends
on the parameters . We identify the -module
with the regular representation of the algebra of functions on a
fiber of a suitable discrete Wronski map. If , we study the action
of on a space of singular vectors of a certain
weight. Again, we identify the -module with the
regular representation of the algebra of functions on a fiber of another
suitable discrete Wronski map.
These results we announced earlier in relation with a description of the
quantum equivariant cohomology of the cotangent bundle of a partial flag
variety and a description of commutative subalgebras of the group algebra of a
symmetric group.Comment: Latex, 23 pages, misprints correcte
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