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arXiv · 2210.15312

Graded extensions of Verma modules

Hankyung Ko·Volodymyr Mazorchuk
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Abstract

In this paper, we investigate extensions between graded Verma modules in the BGG category $\mathcal{O}$. In particular, we determine exactly which information about extensions between graded Verma modules is given by the coefficients of the $R$-polynomials. We also give some upper bounds for the dimensions of graded extensions between Verma modules in terms of Kazhdan-Lusztig combinatorics. We completely determine all extensions between Verma module in the regular block of category $\mathcal{O}$ for $\mathfrak{sl}_4$ and construct various ``unexpected'' higher extensions between Verma modules.

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BibTeXRIS

Hankyung Ko, Volodymyr Mazorchuk. 2022-10-27. Graded extensions of Verma modules. https://doi.org/10.1017/s0305004124000239

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