Journal article
Dirac induction for rational Cherednik algebras
- Abstract:
- We introduce the local and global indices of Dirac operators for the rational Cherednik algebra Ht,c(G,h), where G is a complex reflection group acting on a finite-dimensional vector space h. We investigate precise relations between the (local) Dirac index of a simple module in the category O of Ht,c(G,h), the graded G-character of the module, the Euler–Poincaré pairing, and the composition series polynomials for standard modules. In the global theory, we introduce integral-reflection modules for Ht,c(G,h) constructed from finite-dimensional G-modules. We define and compute the index of a Dirac operator on the integral-reflection module and show that the index is, in a sense, independent of the parameter function c. The study of the kernel of these global Dirac operators leads naturally to a notion of dualised generalised Dunkl–Opdam operators.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, 501.7KB, Terms of use)
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- Publisher copy:
- 10.1093/imrn/rny153
Authors
- Publisher:
- Oxford University Press
- Journal:
- International Mathematics Research Notices More from this journal
- Volume:
- 2020
- Issue:
- 17
- Pages:
- 5155–5214
- Publication date:
- 2018-07-05
- Acceptance date:
- 2018-06-08
- DOI:
- EISSN:
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1687-0247
- ISSN:
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1073-7928
- Language:
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English
- Keywords:
- Pubs id:
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856669
- Local pid:
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pubs:856669
- Deposit date:
-
2020-05-08
Terms of use
- Copyright holder:
- Ciubotaru and De Martino
- Copyright date:
- 2018
- Rights statement:
- © The Author(s) 2018. Published by Oxford University Press.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Oxford University Press at https://doi.org/10.1093/imrn/rny153
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