Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Quantum affine modules for non-twisted Affine Kac-Moody algebras


Authors: V. Futorny, J. T. Hartwig and E. A. Wilson
Journal: Proc. Amer. Math. Soc. 143 (2015), 5159-5171
MSC (2010): Primary 17B37; Secondary 17B67, 17B10
DOI: https://doi.org/10.1090/proc/12663
Published electronically: June 18, 2015
MathSciNet review: 3411134
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct new irreducible weight modules over quantum affine algebras of type I with all weight spaces infinite dimensional. These modules are obtained by parabolic induction from irreducible modules over the Heisenberg subalgebra.


References [Enhancements On Off] (What's this?)

  • [1] Jonathan Beck, Braid group action and quantum affine algebras, Comm. Math. Phys. 165 (1994), no. 3, 555-568. MR 1301623 (95i:17011)
  • [2] Viktor Bekkert, Georgia Benkart, and Vyacheslav Futorny, Weight modules for Weyl algebras, Kac-Moody Lie algebras and related topics, Contemp. Math., vol. 343, Amer. Math. Soc., Providence, RI, 2004, pp. 17-42. MR 2056678 (2005m:16032), https://doi.org/10.1090/conm/343/06182
  • [3] Viktor Bekkert, Georgia Benkart, Vyacheslav Futorny, and Iryna Kashuba, New irreducible modules for Heisenberg and affine Lie algebras, J. Algebra 373 (2013), 284-298. MR 2995027, https://doi.org/10.1016/j.jalgebra.2012.09.035
  • [4] Ben Cox, Vyacheslav Futorny, and Kailash C. Misra, An imaginary PBW basis for quantum affine algebras of type 1, J. Pure Appl. Algebra 219 (2015), no. 1, 83-100. MR 3240825, https://doi.org/10.1016/j.jpaa.2014.04.011
  • [5] V. G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Dokl. Akad. Nauk SSSR 283 (1985), no. 5, 1060-1064 (Russian). MR 802128 (87h:58080)
  • [6] V. Futorny, D. Grantcharov, V. Mazorchuk, Weight modules over infinite dimensional Weyl algebras,Proceedings of the American Mathematical Society, to appear.
  • [7] Vyacheslav M. Futorny, Representations of affine Lie algebras, Queen's Papers in Pure and Applied Mathematics, vol. 106, Queen's University, Kingston, ON, 1997. MR 1627814 (99f:17006)
  • [8] V. M. Futorny, Imaginary Verma modules for affine Lie algebras, Canad. Math. Bull. 37 (1994), no. 2, 213-218. MR 1275706 (95a:17030), https://doi.org/10.4153/CMB-1994-031-9
  • [9] V. Futorny and I. Kashuba, Generalized Loop Modules for Affine Kac-Moody Algebras, Lecture Notes, to appear.
  • [10] Vyacheslav Futorny and Iryna Kashuba, Induced modules for affine Lie algebras, SIGMA Symmetry Integrability Geom. Methods Appl. 5 (2009), Paper 026, 14. MR 2506186 (2010g:17032), https://doi.org/10.3842/SIGMA.2009.026
  • [11] H. P. Jakobsen and V. G. Kac, A new class of unitarizable highest weight representations of infinite-dimensional Lie algebras, Nonlinear equations in classical and quantum field theory (Meudon/Paris, 1983/1984) Lecture Notes in Phys., vol. 226, Springer, Berlin, 1985, pp. 1-20. MR 802097 (87g:17020), https://doi.org/10.1007/3-540-15213-X_67
  • [12] Victor G. Kac, Infinite-dimensional Lie algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. MR 1104219 (92k:17038)
  • [13] G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), no. 2, 237-249. MR 954661 (89k:17029), https://doi.org/10.1016/0001-8708(88)90056-4

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 17B37, 17B67, 17B10

Retrieve articles in all journals with MSC (2010): 17B37, 17B67, 17B10


Additional Information

V. Futorny
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo SP, Brazil
Email: futorny@ime.usp.br

J. T. Hartwig
Affiliation: Department of Mathematics,University of California Riverside, Riverside, California 92521
Email: hartwig@math.ucr.edu

E. A. Wilson
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854-8019
Email: eaw132@scarletmail.rutgers.edu

DOI: https://doi.org/10.1090/proc/12663
Received by editor(s): May 20, 2014
Received by editor(s) in revised form: October 23, 2014
Published electronically: June 18, 2015
Communicated by: Kailash Misra
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society