On the composition structure of the twisted Verma modules for $\mathfrak{sl}(3,\mathbb{C})$

Libor Krizka; Petr Somberg

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arXiv · 1509.00646

On the composition structure of the twisted Verma modules for $\mathfrak{sl}(3,\mathbb{C})$

Libor Krizka·Petr Somberg

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Abstract

We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra $\mathfrak{sl}(3, \mathbb{C})$, including the explicit structure of singular vectors for both $\mathfrak{sl}(3, \mathbb{C})$ and one of its Lie subalgebras $\mathfrak{sl}(2, \mathbb{C})$, and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as $\mathrm{D}$-modules on the Schubert cells in the full flag manifold for $\mathrm{SL}(3, \mathbb{C})$.

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BibTeX RIS

Libor Krizka, Petr Somberg. 2015-09-02. On the composition structure of the twisted Verma modules for $\mathfrak{sl}(3,\mathbb{C})$. https://arxiv.org/abs/1509.00646

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