منابع مشابه
Twisting the quantum grassmannian
In contrast to the classical and semiclassical settings, the Coxeter element (12 . . . n) which cycles the columns of an m×n matrix does not determine an automorphism of the quantum grassmannian. Here, we show that this cycling can be obtained by defining a cocycle twist. A consequence is that the torus invariant prime ideals of the quantum grassmannian are permuted by the action of the Coxeter...
متن کاملCyclic orders on the quantum grassmannian
The quantum grassmannian is known to be a graded quantum algebra with a straightening law when the poset of generating quantum minors is endowed with the standard partial ordering. In this paper it is shown that this result remains true when the ordering is subjected to cyclic shifts. The method involves proving that noncommutative dehomogenisation is possible at any consecutive quantum minor. ...
متن کاملPrime ideals in the quantum grassmannian
We consider quantum Schubert cells in the quantum grassmannian and give a cell decomposition of the prime spectrum via the Schubert cells. As a consequence, we show that all primes are completely prime in the generic case where the deformation parameter q is not a root of unity. There is a natural torus action of H = (k *) n on G q (m, n) and the cell decomposition of the set of H-primes leads ...
متن کاملQuantum Deformation of the Grassmannian Manifold
Ž . In this paper we work out a deformation of G r, n , the grassmannian of r-subspaces in a vector space of dimension n over a field k of characteristic 0. Ž . Ž . G r, n is deformed as an homogeneous space for SL k , the special linear group n n w Ž .x Ž . of k ; this means that k G r, n , the coordinate ring of G r, n , gets deformed w x Ž . together with with the coaction of k SL , the coor...
متن کاملA Sagbi Basis for the Quantum Grassmannian
The maximal minors of a p× (m+p)-matrix of univariate polynomials of degree n with indeterminate coefficients are themselves polynomials of degree np. The subalgebra generated by their coefficients is the coordinate ring of the quantum Grassmannian, a singular compactification of the space of rational curves of degree np in the Grassmannian of p-planes in (m + p)-space. These subalgebra generat...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10478-1