Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analogues of Lusztig's higher order relations for the q-Onsager algebra   Let $A,A^*$ be the generators of the $q-$Onsager algebra. Analogues of
Lusztig's $r-th$ higher order relations are proposed. In a first part, based on
the properties of tridiagonal pairs of $q-$Racah type which satisfy the
defining relations of the $q-$Onsager algebra, higher order relations are
derived for $r$ generic. The coefficients entering in the relations are
determined from a two-variable polynomial generating function. In a second
part, it is conjectured that $A,A^*$ satisfy the higher order relations
previously obtained. The conjecture is proven for $r=2,3$. For $r$ generic,
using an inductive argument recursive formulae for the coefficients are
derived. The conjecture is checked for several values of $r\geq 4$.
Consequences for coideal subalgebras and integrable systems with boundaries at
$q$ a root of unity are pointed out.

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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th