Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $k$-positivity of dual canonical basis elements from 1324- and
  2143-avoiding Kazhdan-Lusztig immanants   In this note, we show that certain dual canonical basis elements of
$\mathbb{C}[SL_m]$ are positive when evaluated on $k$-positive matrices,
matrices whose minors of size $k \times k$ and smaller are positive. Skandera
showed that all dual canonical basis elements of $\mathbb{C}[SL_m]$ can be
written in terms of Kazhdan-Lusztig immanants, which were introduced by Rhoades
and Skandera. We focus on the basis elements which are expressed in terms of
Kazhdan-Lusztig immanants indexed by 1324- and 2143-avoiding permutations. This
extends previous work of the authors on Kazhdan-Lusztig immanants and uses
similar tools, namely Lewis Carroll's identity (also known as the
Desnanot-Jacobi identity).

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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph