Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Whittaker Modules for Generalized Weyl Algebras   We investigate Whittaker modules for generalized Weyl algebras, a class of
associative algebras which includes the quantum plane, Weyl algebras, the
universal enveloping algebra of sl_2 and of Heisenberg Lie algebras, Smith's
generalizations of U(sl_2), various quantum analogues of these algebras, and
many others. We show that the Whittaker modules V = Aw of the generalized Weyl
algebra A = R(phi,t) are in bijection with the phi-stable left ideals of R. We
determine the annihilator Ann_A(w) of the cyclic generator w of V. We also
describe the annihilator ideal Ann_A(V) under certain assumptions that hold for
most of the examples mentioned above. As one special case, we recover Kostant's
well-known results on Whittaker modules and their associated annihilators for
U(sl_2).

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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg