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IRREDUCIBLE REPRESENTATIONS OF THE HAMILTONIAN ALGEBRA H(2r;n)

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  02 August 2011

YU-FENG YAO  and
BIN SHU
YU-FENG YAO*
Affiliation:
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, PR China (email: yaoyufeng139@sina.com, yfyao@shmtu.edu.cn)
BIN SHU
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, PR China (email: bshu@math.ecnu.edu.cn)
*
✉For correspondence; e-mail: yfyao@shmtu.edu.cn
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Abstract

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Let L=H(2r;n) be a graded Lie algebra of Hamiltonian type in the Cartan type series over an algebraically closed field of characteristic p>2. In the generalized restricted Lie algebra setup, any irreducible representation of L corresponds uniquely to a (generalized) p-character χ. When the height of χ is no more than min {pni−pni−1∣i=1,2,…,2r}−2, the corresponding irreducible representations are proved to be induced from irreducible representations of the distinguished maximal subalgebra L0 with the aid of an analogy of Skryabin’s category ℭ for the generalized Jacobson–Witt algebras and modulo finitely many exceptional cases. Since the exceptional simple modules have been classified, we can then give a full description of the irreducible representations with p-characters of height below this number.

Keywords

Cartan type Lie algebrasgeneralized restricted Lie algebrasHamiltonian algebrasℭ-categoryexceptional modules

MSC classification

Secondary: 17B10: Representations, algebraic theory (weights) 17B70: Graded Lie (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 3 , June 2011 , pp. 403 - 430
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work is partially supported by the NSF of China (No. 10871067), the PCSIRT of China and the Science and Technology Program of Shanghai Maritime University (No. 20110053).

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