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• W2951341092 abstract "The main aim of this paper is to establish a deep link between the totally nonnegative grassmannian and the grassmannian. More precisely, under the assumption that the deformation parameter $q$ is transcendental, we show that quantum positroids are completely prime ideals in the grassmannian $A$. As a consequence, we obtain that torus-invariant prime ideals in the grassmannian are generated by polynormal sequences of Plucker 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." @default.
• W2951341092 created "2019-06-27" @default.
• W2951341092 creator A5070317627 @default.
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• W2951341092 date "2019-06-14" @default.
• W2951341092 modified "2023-09-27" @default.
• W2951341092 title "Total positivity is a quantum phenomenon: the grassmannian case" @default.
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