Imaginary Verma Modules for the Extended Affine Lie Algebra sl₂(ℂ_q)

References

• Allison , B. , Azam , S. , Berman , S. , Gao , Y. and Pianzola , A. 1997 . Extended Affine Lie Algebras and Their Root Systems . Memoirs of the AMS , 126 ( 603 )
   Google Scholar
• Berman , S. and Billig , Y. 1999 . Irreducible representations for toroidal Lie algebras . Journal of Algebra , 221 : 188 – 231 .
   Google Scholar
• Berman , S. and Cox , B. 1994 . Enveloping algebras and representations of toroidal Lie algebras . Pacific J. Math. , 165 : 239 – 269 .
   Google Scholar
• Berman , S. , Gao , Y. and Krylyuk , Y. 1996 . Quantum tori and the structure of elliptic quasi-simple Lie algebras . J. Funct. Anal. , 135 : 339 – 389 .
   Google Scholar
• Berman , S. and Szmigielski , J. 1998 . “ Principal realization for extended affine Lie algebra of type sl 2 with coordinates in a simple quantum torus with two variables ” . In Recent Developments in Quantum Affine Algebras and Related Topics NC : Raleigh . Contemporary Math.; Amer. Math. Soc.: Providence, RI, 1999, 248, 39–67
   Google Scholar
• Billig , Y. 1998 . Principal vertex operator representations for toroidal Lie algebras . Journal of Math. Physics , 39 : 3844 – 3864 .
   Google Scholar
• Cox, B. Fock space realization of imaginary Verma modules . Transactions of the AMS (to appear) ,
   Google Scholar
• Cox , B. and Futorny , V. 2001 . Borel subalgebras and categories of highest weight modules for toroidal Lie algebras . Journal of Algebra , 236 : 1 – 28 .
   Google Scholar
• Eswara Rao , S. , Moody , R. and Yokonuma , T. 1990 . Toroidal Lie algebras and vertex representations . Geom. Ded. , 35 : 283 – 307 .
   Google Scholar
• Eswara Rao , S. , Moody , R. and Yokonuma , T. 1992 . Lie algebras arising from vertex operator representations . Nova J. Algebra and Geometry , 1 : 15 – 57 .
   Google Scholar
• Eswara Rao , S. and Moody , R. 1994 . Vertex representations for n-toroidal Lie algebras and a generalization of the Virasoro algebras . Commun. Math. Physics , 159 : 239 – 264 .
   Google Scholar
• Futorny , V. 1994 . Imaginary Verma modules . Canad. Math. Bull. , 37 ( 2 ) : 213 – 218 .
   Google Scholar
• Futorny , V. and Kashuba , I. 1999 . Verma type modules for toroidal Lie algebras . Commun. in Algebra , 27 ( 8 ) : 3979 – 3991 .
   Google Scholar
• Gao , Y. 2000a . Representations of extended affine Lie algebras coordinatized by certain quantum tori . Compositio Mathematica , 123 ( 1 ) : 1 – 25 .
   Google Scholar
• Gao , Y. 2000b . Vertex operators arizing from the homogeneous realization for ĝl N . Commun. Math. Phys. , 211 : 745 – 777 .
   Google Scholar
• Kac , V. 1990 . Infinite-dimensional Lie algebras , 3 Cambridge, NJ : Cambridge University Press .
   Google Scholar
• Manin , Y. 1991 . Topics in Noncommutative Geometry Princeton, NJ : Princeton University Press .
   Google Scholar
• Tan , S. 1999a . Principal construction of the toroidal Lie algebra of type A 1 . Math. Z. , 230 : 621 – 657 .
   Google Scholar
• Tan , S. 1999b . Vertex operator representations for toroidal Lie algebra of type B l . Commun. in Algebra , 27 ( 8 ) : 3593 – 3618 .
   Google Scholar
• Tan , S. 1999c . TKK algebras and vertex operator representations . Journal of Algebra , 211 : 298 – 342 .
   Google Scholar
• Wakimoto, M. Extended affine Lie algebras and a certain series of Hermitian representations. Preprint, 1985
   Google Scholar
• Yamada , H. 1989 . Extended affine Lie algebras and their vertex representations . Publ. RIMS, Kyoto Univ. , 25 : 587 – 603 .
   Google Scholar