Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Generalized Verma Modules and Multilinear Intertwining Differential
  Operators   The present paper contains two interrelated developments. First, are proposed
new generalized Verma modules. They are called k-Verma modules, k\in N, and
coincide with the usual Verma modules for k=1. As a vector space a k-Verma
module is isomorphic to the symmetric tensor product of k copies of the
universal enveloping algebra U(g^-), where g^- is the subalgebra of lowering
generators in the standard triangular decomposition of a simple Lie algebra g =
g^+ \oplus h \oplus g^- . The second development is the proposal of a procedure
for the construction of multilinear intertwining differential operators for
semisimple Lie groups G . This procedure uses k-Verma modules and coincides for
k=1 with a procedure for the construction of linear intertwining differential
operators. For all k central role is played by the singular vectors of the
k-Verma modules. Explicit formulae for series of such singular vectors are
given. Using these are given explicitly many new examples of multilinear
intertwining differential operators. In particular, for G = SL(2,R) are given
explicitly all bilinear intertwining differential operators. Using the latter,
as an application are constructed (n/2)-differentials for all n\in 2N, the
ordinary Schwarzian being the case n=4. As another application, in a Note Added
we propose a new hierarchy of nonlinear equations, the lowest member being the
KdV equation.

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The categories of this paper are: hep-lat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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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: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: cs