Whittaker Categories and Whittaker Modules for Lie Superalgebras

REFERENCES

• Batra , P. , Mazorchuk , V. ( 2011 ). Blocks and modules for Whittaker pairs . J. Pure Appl. Algebra 215 : 1552 – 1568 .
   Web of Science ®Google Scholar
• Benkart , G. , Ondrus , M. ( 2009 ). Whittaker modules for generalized Weyl algebras . Represent. Theory 13 : 141 – 164 .
   Google Scholar
• Bourbaki , N. ( 2002 ). Lie groups and Lie algebras . Chapters 4–6, Lie Groups and Lie Algebras, Elements of Mathematics (Berlin), Springer-Verlag, Berlin .
   Google Scholar
• Bourbaki , N. ( 2002 ). Lie groups and Lie algebras . Chapters 7–9, Lie Groups and Lie Algebras, Elements of Mathematics (Berlin), Springer-Verlag, Berlin .
   Google Scholar
• Cheng , S. J. , Wang , W. ( 2012 ). Dualities and Representations of Lie Superalgebras . Graduate Studies in Mathematics . Vol. 144 . Providence , RI : American Mathematical Society .
   Google Scholar
• Christodoulopoulou , K. ( 2008 ). Whittaker modules for Heisenberg algebras and imaginary Whittaker modules for affine Lie algebras . J. Algebra 320 : 2871 – 2890 .
   Web of Science ®Google Scholar
• Gorelik , M. ( 2000 ). On the ghost center of Lie superalgebras . Ann. Inst. Fourier 50 : 1745 – 1764 .
   Web of Science ®Google Scholar
• Gorelik , M. ( 2002 ). Annihilation theorem and separation theorem for basic classical Lie superalgebras Lie superalgebras . J. Amer. Math. Soc. 15 : 113 – 165 .
   Web of Science ®Google Scholar
• Gorelik , M. ( 2002 ). Strongly typical representations of the basic classical Lie superalgebras . J. Amer. Math. Soc. 15 : 167 – 184 .
   Web of Science ®Google Scholar
• Kac , V. G. ( 1977 ). Lie superalgebras . Advances in Math. 26 : 8 – 96 .
   Web of Science ®Google Scholar
• Kostant , B. ( 1978 ). On Whittaker vectors and representation theory . Invent. Math. 48 : 101 – 184 .
   Web of Science ®Google Scholar
• Liu , D. , Wu , Y. , Zhu , L. ( 2010 ). Whittaker modules for the twisted Heisenberg-Virasoro algebra . J. Math. Physics 51 : 023524, 12 p .
   Web of Science ®Google Scholar
• McDowell , E. ( 1985 ). On modules induced from Whittaker modules . J. Algebra 96 : 161 – 177 .
   Web of Science ®Google Scholar
• McDowell , E. ( 1993 ). A module induced from a Whittaker module . Proc. Amer. Math. Soc. 118 : 349 – 354 .
   Web of Science ®Google Scholar
• Miličić , D. , Soergel , W. ( 1997 ). The composition series of modules induced from Whittaker modules . Comment. Math. Helv. 72 : 503 – 520 .
   Web of Science ®Google Scholar
• Musson , I. ( 1997 ). On the center of the enveloping algebra of a classical simple Lie superalgebra . J. Algebra 193 : 75 – 101 .
   Web of Science ®Google Scholar
• Ondrus , M. ( 2005 ). Whittaker modules for U q (𝔰𝔩2) . J. Algebra 289 : 192 – 213 .
   Web of Science ®Google Scholar
• Ondrus , M. , Wiesner , E. ( 2009 ). Whittaker modules for the Virasoro algebra . J. Algebra Appl. 8 : 363 – 377 .
   Web of Science ®Google Scholar
• Serganova , V. ( 2003 ). A reduction method for atypical representations of classical Lie superalgebras . Adv. Math. 180 : 248 – 274 .
   Web of Science ®Google Scholar
• Sergeev , A. ( 1999 ). Irreducible representations of solvable Lie superalgebras . Represent. Theory 3 : 435 – 443 .
   Google Scholar
• Sevostyanov , A. ( 2000 ). Quantum deformation of Whittaker modules and the Toda lattice . Duke Math. J. 105 : 211 – 238 .
   Web of Science ®Google Scholar
• Wang , B. ( 2010 ). Whittaker modules for graded Lie algebras . Algebr. Represent. Theory 1 – 12 .
   Web of Science ®Google Scholar
• Communicated by K. Misra.
   Google Scholar