2019/06/14 by Stéphane Launois, Launois, Stéphane, Tom Lenagan +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.CO #math.QA #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1906.06199
90 pages
arxiv created 2019/06/14 · openalex publication_date 2019/06/14 · arxiv updated 2019/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main aim of this paper is to establish a deep link between the totally nonnegative grassmannian and the quantum grassmannian. More precisely, under the assumption that the deformation parameter q is transcendental, we show that "quantum positroids" are completely prime ideals in the quantum grassmannian A. As a consequence, we obtain that torus-invariant prime ideals in the quantum grassmannian are generated by polynormal sequences of quantum Plücker coordinates and give a combinatorial description of these generating sets. We also give a topological description of the poset of torus-invariant prime ideals in A, and prove a version of the orbit method for torus-invariant objects. Finally, we construct separating Ore sets for all torus-invariant primes in A. The latter is the first step in the Brown-Goodearl strategy to establish the orbit method for (quantum) grassmannians.