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

Published online by Cambridge University Press:  02 August 2011

YU-FENG YAO*
Affiliation:
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, PR China (email: [email protected], [email protected])
BIN SHU
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, PR China (email: [email protected])
*
For correspondence; e-mail: [email protected]
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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 {pnipni−1i=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.

Type
Research Article
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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