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Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations
Cornell University
,
2013.
No. arXiv:1306.1292.
We introduce the notion of a favourable module for a complex unipotent algebraic group, whose properties are governed by the combinatorics of an associated polytope. We describe two filtrations of the module, one given by the total degree on the PBW basis of the corresponding Lie algebra, the other by fixing a homogeneous monomial order on the PBW basis. In the favourable case a basis of the module is parameterized by the lattice points of a normal polytope. The filtrations induce flat degenerations of the corresponding flag variety to its abelianized version and to a toric variety, the special fibres of the degenerations being projectively normal and arithmetically Cohen-Macaulay. The polytope itself can be recovered as a Newton-Okounkov body. We conclude the paper by giving classes of examples for favourable modules.
Priority areas:
mathematics
Language:
English
Feigin E., Functional Analysis and Its Applications 2014 Vol. 48 No. 1 P. 59-71
The degenerate Lie group is a semidirect product of the Borel subgroup with the normal
abelian unipotent subgroup.
We introduce a class of the highest weight representations of the degenerate group of type A, generalizing
the PBW-graded representations of the classical group. Following the classical construction
of the flag varieties, we consider the closures of the orbits of the ...
Added: April 30, 2014
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We construct special rational ${\rm gl}_N$ Knizhnik-Zamolodchikov-Bernard
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