2018 / June Volume 13 No.2
Positivity VS Negativity of Canonical Bases
| Published Date |
2018 / June
|
|---|---|
| Title | Positivity VS Negativity of Canonical Bases |
| Author | |
| Keyword | |
| Download | |
| Pagination | 143-198 |
| Abstract | We provide examples
for negativity of structure constants of the stably canonical basis
of modified quantum $\mathfrak{gl}_n$ and an analogous basis of
modified quantum coideal algebra of $\mathfrak{gl}_n$. In contrast,
we construct the canonical basis of the modified quantum coideal
algebra of $\mathfrak{sl}_n$, establish the positivity of its
structure constants, the positivity with respect to a geometric
bilinear form as well as the positivity of its action on the tensor
powers of the natural representation. The matrix coefficients of the
transfer map on these Schur algebras with respect to the canonical
bases are shown to be positive.
Formulas for canonical basis of the iSchur algebra of rank one are obtained.
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| DOI | |
| AMS Subject Classification |
17B37, 14L35, 20G43.
|
| Received |
2016-06-04
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| Accepted |
2016-06-05
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