Stability Conditions for Gelfand–Kirillov Subquotients of Category $\mathcal{O}$

DOI10.1093/IMRN/RNW178zbMATH Open1405.18022arXiv1511.08487OpenAlexW2513503517MaRDI QIDQ4612043

Vinoth Nandakumar

Publication date: 22 January 2019

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: Recently, Anno, Bezrukavnikov and Mirkovic have introduced the notion of a "real variation of stability conditions" (which is related to Bridgeland's stability conditions), and construct an example using categories of coherent sheaves on Springer fibers. Here we construct another example of representation theoretic significance, by studying certain sub-quotients of category O with a fixed Gelfand-Kirillov dimension. We use the braid group action on the derived category of category O, and certain leading coefficient polynomials coming from translation functors. Consequently, we use this to explicitly describe a sub-manifold in the space of Bridgeland stability conditions on these sub-quotient categories, which is a covering space of a hyperplane complement in the dual Cartan.

Full work available at URL: https://arxiv.org/abs/1511.08487

zbMATH Keywords

Gelfand-Kirillov subquotients

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) Modular Lie (super)algebras (17B50)

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