A Borel-Weil theorem for the irreducible quantum flag manifolds
| Autor: | Carotenuto, Alessandro, Garc��a, Fredy D��az, Buachalla, R��amonn �� |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Popis: | We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the irreducible quantum flag manifolds $\mathcal{O}_q(G/L_S)$, generalising previous work of a number of authors (including the first and third authors of this paper) on the quantum Grassmannians $\mathcal{O}_q(\mathrm{Gr}_{n,m})$. As a direct consequence we get a novel noncommutative differential geometric presentation of the quantum coordinate rings $S_q[G/L_S]$ of the irreducible quantum flag manifolds. The proof is formulated in terms of quantum principal bundles, and the recently introduced notion of a principal pair, and uses the Heckenberger and Kolb first-order differential calculus for the quantum Possion homogeneous spaces $\mathcal{O}_q(G/L^{\mathrm{s}}_S)$. 26 pages |
| Databáze: | OpenAIRE |
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