87
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Finite-Dimensional Representations of Twisted Hyper-Loop Algebras

&
Pages 3147-3182 | Received 25 May 2012, Published online: 13 Mar 2014

REFERENCES

  • Beck , J. , Nakajima , H. ( 2004 ). Crystal bases and two-sided cells of quantum affine algebras . Duke Math. J. 123 : 335 – 402 .
  • Bianchi , A. ( 2012 ). Representações de hiperálgebras de laços e álgebras de multicorrentes, Ph.D. Thesis, Unicamp, Campinas, Brazil .
  • Bianchi , A. , Macedo , T. , Moura , A. On Demazure and local Weyl modules for affine hyperalgebras. Preprint:arXiv:1307.4305 .
  • Chari , V. , Fourier , G. , Senesi , P. ( 2008 ). Weyl Modules for the twisted loop algebras . J. Algebra 319 ( 12 ): 5016 – 5038 .
  • Chari , V. , Loktev , S. ( 2006 ). Weyl, Demazure and fusion modules for the current algebra of 𝔰𝔩 r+1 . Adv. in Math. 207 ( 2 ): 928 – 960 .
  • Chari , V. , Pressley , A. ( 2001 ). Weyl modules for classical and quantum affine algebras . Represent. Theory 5 : 191 – 223 .
  • Efrat , I. ( 2006 ). Valuation, Orderings, and Milnor K-Theory . Mathematical Surveys and Monographs AMS, 124 .
  • Fourier , G. , Khandai , T. , Kus , D. , Savage , A. ( 2012 ). Local Weyl modules for equivariant map algebras with free abelian group actions . J. Algebra 350 : 386 – 404 .
  • Fourier , G. , Kus , D. ( 2013 ). Demazure modules and Weyl modules: The twisted current case . To appear in Trans. Amer. Math. Soc. 365 ( 11 ): 6037 – 6064 .
  • Fourier , G. , Littelmann , P. ( 2007 ). Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions . Adv. in Math. 211 ( 2 ): 566 – 593 .
  • Fourier , G. , Manning , N. , Senesi , P. ( 2013 ). Global Weyl modules for the twisted loop algebra . Abh. Math. Semin. Univ. Hambg. 83 ( 1 ): 53 – 82 .
  • Garland , H. ( 1978 ). The arithmetic theory of loop algebras . J. Algebra 53 : 480 – 551 .
  • Humphreys , J. E. ( 1970 ). Introduction to Lie algebras and representation theory. Springer–Verlag, GTM, 9 .
  • Jakelic , D. , Moura , A. ( 2007 ). Finite-dimensional representations of hyper-loop algebras . Pacific J. Math. 233 ( 2 ): 371 – 402 .
  • Jakelic , D. , Moura , A. (2010). Finite-dimensional representations of hyper-loop algebras over non-algebraically closed fields. Algebras and Representation Theory 13(3):271–301.
  • Jakelic , D. , Moura , A. ( 2009 ). On multiplicity problems for finite-dimensional representations of hyper-loop algebras . Contemp. Math. 483 : 147 – 159 .
  • Jantzen , J. ( 1987 ). Representations of Algebraic Groups . Boston : Academic Press .
  • Kac , V. ( 1990 ). Infinite Dimensional Lie Algebras . New York : Cambridge University Press .
  • Kashiwara , M. ( 1994 ). Crystal bases of modified quantized enveloping algebras . Duke Math. J. 73 : 383 – 413 .
  • Kashiwara , M. ( 2002 ). On level zero representations of quantized affine algebras . Duke Math. J. 112 : 117 – 195 .
  • Kostant , B. ( 1966 ). Groups over ℤ . Algebraic Groups and Discontinuous Subgroups, Proc. Symp. Pure Math. IX , Providence : AMS .
  • Mitzman , D. ( 1983 ). Integral bases for affine lie algebras and their universal enveloping algebras . Contemp. Math. 40 .
  • Nakajima , H. ( 2001 ). Quiver varieties and finite-dimensional representations of quantum affine algebras . J. Amer. Math. Soc. 14 : 145 – 238 .
  • Nakajima , H. ( 2004 ). Extremal weight modules of quantum affine algebras . Adv. Stud. Pure Math. 40 : 343 – 369 .
  • Naoi , K. ( 2012 ). Weyl modules, Demazure modules and finite crystals for non-simply laced type . Adv. in Math. 229 ( 2 ): 875 – 934 .
  • Neher , E. , Savage , A. Extensions and block decompositions for finite-dimensional representations of equivariant map algebras, arXiv:1103.4367 .
  • Neher , E. , Savage , A. , Senesi , P. ( 2012 ). Irreducible finite-dimensional representations of equivariant map algebras . Trans. Amer. Math. Soc. 364 ( 5 ): 2619 – 2646 .
  • Prevost , S. ( 1992 ). Vertex algebras and integral Bases for the enveloping algebras of affine lie algebras . Mem. Math. Amer. Soc., 466 .
  • Senesi , P. ( 2010 ). The block decomposition of finite-dimensional representations of twisted loop algebras . Pacific J. Math. 244 ( 2 ): 355 – 357 .
  • Serre , J.-P. ( 1980 ). Local Fields . Springer-Verlag GTM 67 .
  • Communicated by K. Misra.

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.