Abstract
In [B. Leclerc, A. Zelevinsky, Quasicommuting families of quantum Plücker coordinates, in: Kirillov's Seminar on Representation Theory, in: Amer. Math. Soc. Transl. (2), vol. 181, Amer. Math. Soc., Providence, RI, 1998, pp. 85–108], a combinatorial criterion for quasi-commutativity is established for pairs of quantum Plücker coordinates in the quantized coordinate algebra C q [ F ] of the flag variety of type A. This paper attempts to generalize these results by producing necessary and sufficient conditions for pairs of quantum minors in the quantized coordinate algebra C q [ Mat k × m ] to quasi-commute. In addition, we study the combinatorics of maximal (by inclusion) families of pairwise quasi-commuting quantum minors and pose relevant conjectures.
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