340 research outputs found
Pfaffians and Shuffling Relations for the Spin Module
We present explicit formulas for a set of generators of the ideal of
relations among the pfaffians of the principal minors of the antisymmetric
matrices of fixed dimension. These formulas have an interpretation in terms of
the standard monomial theory for the spin module of orthogonal groups.Comment: 10 page
The ring of sections of a complete symmetric variety
We study the ring of sections A(X) of a complete symmetric variety X, that is
of the wonderful completion of G/H where G is an adjoint semi-simple group and
H is the fixed subgroup for an involutorial automorphism of G. We find
generators for Pic(X), we generalize the PRV conjecture to complete symmetric
varieties and construct a standard monomial theory for A(X) that is compatible
with G orbit closures in X. This gives a degeneration result and the rational
singularityness for A(X).Comment: 15 pages, Late
Pl\:ucker relations and spherical varieties: application to model varieties
A general framework for the reduction of the equations defining classes of
spherical varieties to (maybe infinite dimensional) grassmannians is proposed.
This is applied to model varieties of type A, B and C; in particular a standard
monomial theory for these varieties is presented.Comment: 15 pages, accepted for publication in Transformation Group
Equations defining symmetric varieties and affine Grassmannians
Let be a simple involution of an algebraic semisimple group and
let be the subgroup of of points fixed by . If the restricted
root system is of type , or and is simply connected or if the
restricted root system is of type and is adjoint, then we describe a
standard monomial theory and the equations for the coordinate ring
using the standard monomial theory and the Pl\"ucker relations of an
appropriate (maybe infinite dimensional) Grassmann variety.Comment: 48 page
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