171
Views
11
CrossRef citations to date
0
Altmetric
Original Articles

Whittaker Modules over Generalized Virasoro Algebras

&
Pages 3222-3231 | Received 12 May 2010, Published online: 07 Oct 2011

REFERENCES

  • Arnal , D. , Pinczon , G. ( 1974 ). On algebraically irreducible representations of the Lie algebra sl(2) . J. Mathematical Phys. 15 : 350 – 359 .
  • Backelin , E. ( 1997 ). Representation of the category O in Whittaker categories . Internat. Math. Res. Notices 4 : 153 – 172 .
  • Block , R. ( 1981 ). The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra . Adv. Math. 39 : 69 – 110 .
  • Batra , P. , Guo , X. , Lu , R. , Zhao , K. ( 2009 ). Highest weight modules over the pre-exp-polynomial algebras . J. Algebra 322 : 4163 – 4180 .
  • Batra , P. , Mazorchuk , V. Blocks and modules for Whittaker pairs. arXiv:0910.3540v1.
  • Benkart , G. , Ondrus , M. ( 2009 ). Whittaker modules for generalized Weyl algebras . Represent. Theory 13 : 141 – 164 .
  • Christodoupoulou , K. ( 2008 ). Whittaker modules for Heisenberg algebras and imaginary Whittaker modules for affine Lie algebras . J. Algebra 320 : 2871 – 2890 .
  • Guo , X. , Liu , X. , Zhao , K. Harish–Chandra modules over the ℚ Heisenberg Virasoro algebra . Journal Aust. Math. Soc. Accepted.
  • Guo , X. , Lu , R. , Zhao , K. Classification of irreducible Harish–Chandra modules over the generalized Virasoro algebras . arXiv:math/0607614 .
  • Guo , X. , Lu , R. , Zhao , K. Simple Harish–Chandra modules, intermediate series modules and Verma modules over the loop-Virasoro algebra. Forum Math. in press.
  • Hu , J. , Wang , X. , Zhao , K. ( 2003 ). Verma modules over generalized Virasoro algebras Vir[G] . J. Pure Appl. Algebra 177 : 61 – 69 .
  • Khomenko , O. , Mazorchuk , V. ( 2004 ). Structure of modules induced from simple modules with minimal annihilator . Canad. J. Math. 56 : 293 – 309 .
  • Kostant , B. ( 1978 ). On Whittaker vectors and representation theory . Invent. Math. 48 : 101 – 184 .
  • Li , J. , Wang , B. Whittaker Modules For The W-algebra W(2, 2), arXiv:0902.1592 .
  • Liu , D. , Wu , Y. , Zhu , L. Whittaker Modules for the twisted Heisenberg-Virasoro Algebra . Preprint arXiv:0902.4074.
  • Lu , R. , Zhao , K. ( 2006 ). Classification of irreducible weight modules over higher rank Virasoro algebras . Advances in Math. 201 : 630 – 656 .
  • Mazorchuk , V. ( 2000 ). Classification of simple Harish–Chandra modules over ℚ Virasoro algebra . Math. Nachr. 209 : 171 – 177 .
  • Mazorchuk , V. ( 1999 ). Verma modules over generalized Witt algebras . Compositio. Math. 115 : 21 – 35 .
  • Mazorchuk , V. Lectures on sl 2 Modules. Imperial College Press , 2009 .
  • McDowell , E. ( 1985 ). On modules induced from Whittaker modules . J. Algebra 96 : 161 – 177 .
  • McDowell , E. ( 1993 ). A module induced from a Whittaker module . Proc. Amer. Math. Soc. 118 : 349 – 354 .
  • Milicic , D. , Soergel , W. ( 1997 ). The composition series of modules induced from Whittaker modules . Comment. Math. Helv. 72 : 503 – 520 .
  • Milicic , D. , Soergel , W. Twisted Harish–Chandra sheaves and Whittaker modules: The non-degenerate case . Preprint. http://home.mathematik.uni-freiburg.de/soergel/ .
  • Ondrus , M. ( 2005 ). Whittaker modules for Uq(sl2) . J. Algebra 289 : 192 – 213 .
  • Ondrus , M. ( 2007 ). Tensor products and Whittaker vectors for quantum groups . Comm. Algebra 35 : 2506 – 2523 .
  • Ondrus , M. Wiesner , E. ( 2009 ). Whittaker Modules for the Virasoro Algebra . J. Algebra Appl. 8 : 363 – 377 .
  • Patera , J. Zassenhaus , H. ( 1991 ). The higher rank Virasoro algebras . Commun. Math. Phys. 136 : 1 – 14 .
  • Sevostyanov , A. ( 2000 ). Quantum deformation of Whittaker modules and the Toda lattice . Duke Math. J. 105 : 211 – 238 .
  • Su , Y. ( 2001 ). Simple modules over the high rank Virasoro algebras . Comm. Algebra 29 : 2067 – 2080 .
  • Su , Y. ( 2003 ). Classification of Harish–Chandra modules over the higher rank Virasoro algebras . Comm. Math. Phys. 240 : 539 – 551 .
  • Tang , X. ( 2007 ). On Whittaker modules over a class of algebras similar to U(sl2) . Front. Math. China 2 : 127 – 142 .
  • Tan , S. , Zhang , X. Whittaker modules for the Schrodinger-Virasoro algebra . Preprint arXiv:0812.3245 .
  • Wang , B. Whittaker Modules for Graded Lie Algebras . Preprint arXiv:0902.3801 .
  • Wang , B. , Zhu , X. Whittaker modules for a Lie algebra of Block type . Preprint arXiv:0907.0773 .
  • Communicated by M. Bresar.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.