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Original scientific paper
https://doi.org/10.3336/gm.53.2.05

Computing the associated cycles of certain Harish-Chandra modules

Salah Mehdi ; Institut Elie Cartan de Lorraine, CNRS - UMR 7502, Université de Lorraine, Metz, F-57045, France
Pavle Pandžić ; Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
David Vogan ; Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Roger Zierau ; Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078, USA

Fulltext: english, pdf (399 KB) pages 275-330 downloads: 206* cite
APA 6th Edition
Mehdi, S., Pandžić, P., Vogan, D. & Zierau, R. (2018). Computing the associated cycles of certain Harish-Chandra modules. Glasnik matematički, 53 (2), 275-330. https://doi.org/10.3336/gm.53.2.05
MLA 8th Edition
Mehdi, Salah, et al. "Computing the associated cycles of certain Harish-Chandra modules." Glasnik matematički, vol. 53, no. 2, 2018, pp. 275-330. https://doi.org/10.3336/gm.53.2.05. Accessed 29 Nov. 2021.
Chicago 17th Edition
Mehdi, Salah, Pavle Pandžić, David Vogan and Roger Zierau. "Computing the associated cycles of certain Harish-Chandra modules." Glasnik matematički 53, no. 2 (2018): 275-330. https://doi.org/10.3336/gm.53.2.05
Harvard
Mehdi, S., et al. (2018). 'Computing the associated cycles of certain Harish-Chandra modules', Glasnik matematički, 53(2), pp. 275-330. https://doi.org/10.3336/gm.53.2.05
Vancouver
Mehdi S, Pandžić P, Vogan D, Zierau R. Computing the associated cycles of certain Harish-Chandra modules. Glasnik matematički [Internet]. 2018 [cited 2021 November 29];53(2):275-330. https://doi.org/10.3336/gm.53.2.05
IEEE
S. Mehdi, P. Pandžić, D. Vogan and R. Zierau, "Computing the associated cycles of certain Harish-Chandra modules", Glasnik matematički, vol.53, no. 2, pp. 275-330, 2018. [Online]. https://doi.org/10.3336/gm.53.2.05

Abstracts
Let Gℝ be a simple real linear Lie group with maximal compact subgroup Kℝ and assume that rank(Gℝ)=rank(Kℝ). In [17] we proved that for any representation X of Gelfand-Kirillov dimension 1/2dim(Gℝ/Kℝ), the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing X is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In this paper we compute these coefficients explicitly.

Keywords
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Hrčak ID: 214476

URI
https://hrcak.srce.hr/214476

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