Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The symmetric invariants of the centralizers and Slodowy grading   Let g be a finite-dimensional simple Lie algebra of rank r over an
algebraically closed field of characteristic zero, and let e be a nilpotent
element of g. Denote by g^e the centralizer of e in g and by S(g^e)^{g^e} the
algebra of symmetric invariants of g^e. We say that e is good if the
nullvariety of some r homogeneous elements of S(g^e)^{g^e} in the dual of g^{e}
has codimension r. If e is good then S(g^e)^{g^e} is polynomial. The main
result of this paper stipulates that if for some homogeneous generators of
S(g^e)^{g^e}, the initial homogeneous component of their restrictions to e+g^f
are algebraically independent, with (e,h,f) an sl2-triple of g, then e is good.
As applications, we obtain new examples of nilpotent elements that verify the
above polynomiality condition, in in simple Lie algebras of both classical and
exceptional types. We also give a counter-example in type D_7.

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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg