Affinization of category $\mathcal {O}$ for quantum groups
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- by E. Mukhin and C. A. S. Young PDF
- Trans. Amer. Math. Soc. 366 (2014), 4815-4847 Request permission
Abstract:
Let $\mathfrak {g}$ be a simple Lie algebra. We consider the category $\hat {\mathcal {O}}$ of those modules over the affine quantum group $U_q(\widehat {\mathfrak {g}})$ whose $U_q(\mathfrak {g})$-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category $\hat {\mathcal {O}}$. In particular, we define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.References
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Additional Information
- E. Mukhin
- Affiliation: Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, LD 270, Indianapolis, Indiana 46202
- MR Author ID: 317134
- Email: mukhin@math.iupui.edu
- C. A. S. Young
- Affiliation: School of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield AL10 9AB, United Kingdom
- Email: charlesyoung@cantab.net
- Received by editor(s): April 24, 2012
- Received by editor(s) in revised form: November 9, 2012, and November 23, 2012
- Published electronically: May 5, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 4815-4847
- MSC (2010): Primary 17B37; Secondary 81R50
- DOI: https://doi.org/10.1090/S0002-9947-2014-06039-X
- MathSciNet review: 3217701