Twisting the quantum grassmannian

TL;DR

This paper demonstrates that a cocycle twist can replicate the cycling action of the Coxeter element on the quantum grassmannian, revealing new symmetries and permutations of prime ideals in the quantum setting.

Contribution

It introduces a cocycle twist to emulate the Coxeter element's action on the quantum grassmannian, extending classical symmetries to the quantum realm.

Findings

Cocycle twist reproduces Coxeter cycling in quantum grassmannian.

Permutation of torus invariant prime ideals by Coxeter element.

Quantum analogue of classical permutation of Lusztig strata.

Abstract

In contrast to the classical and semiclassical settings, the Coxeter element (12...n) which cycles the columns of an mxn 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 element (12...n); we view this as a quantum analogue of the recent result of Knutson, Lam and Speyer that the Lusztig strata of the classical grassmannian are permuted by (12...n).