9 citations · 12 across the 4 of their papers we have counts for
7 papers
Scaffoldings of Totally Positive Matrices and Line Insertion
Karel Casteels
Given a totally positive matrix, can one insert a line (row or column) between two given lines while maintaining total positivity? This question was first posed and solved by Johns…
From Grassmann necklaces to restricted permutations and back again
Karel Casteels, Siân Fryer
We study the commutative algebras appearing in Brown and Goodearl's extension of the -stratification framework, and show that if is the single parameter q…
Quantum Matrices by Paths
Karel Casteels
We study, from a combinatorial viewpoint, the quantized coordinate ring of mxn matrices over an infinite field K (also called quantum matrices) and its torus-invariant prime ideals…
Enumeration of torus-invariant strata with respect to dimension in the big cell of the quantum minuscule Grassmannian of type B_n
Jason Bell, Karel Casteels, Stéphane Launois
The aim of this article is to give explicit formulae for various generating functions, including the generating function of torus-invariant primitive ideals in the big cell of the…
Enumeration of $\C{H}$-strata in quantum matrices with respect to dimension
Jason Bell, Karel Casteels, Stéphane Launois
We present a combinatorial method to determine the dimension of $\C{H}$-strata in the algebra of quantum matrices $\Oq$ as follows. To a given $\C{H}$-stratum we associ…
Primitive ideals in quantum Schubert cells: dimension of the strata
Jason Bell, Karel Casteels, Stéphane Launois
The aim of this paper is to study the representation theory of quantum Schubert cells. Let $\g$ be a simple complex Lie algebra. To each element of the Weyl group of $\g$,…