Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On canonical bases of Letzter algebra $\mathbf
  U^{\imath}(\mathfrak{sl}_2)$   Let $\mathbf U^{\imath}\equiv\mathbf U^{\imath} (\mathfrak{sl}_2)$ be
Letzter's coideal subalgebra of quantum $\mathfrak{sl}_2$ corresponding to the
symmetric pair $(\mathfrak{sl}_2(\mathbb C),\mathbb C)$. As a subalgebra of
quantum $\mathfrak{sl}_2$, $\mathbf U^{\imath}$ is generated by the sum
$\mathbf E + v\mathbf K\mathbf F+\mathbf K$ of standard generators, and hence
can be identified with the polynomial ring $\mathbb Q(v)[t]$. In [BW13] and
[LW18], two distinguished bases, called $\imath$canonical bases, are
constructed inside the modified form of $\mathbf U^{\imath}$ via algebraic and
geometric approaches respectively. The modified form of $\mathbf U^{\imath}$
can be identified with a direct sum of two copies of $\mathbf
U^{\imath}\cong\mathbb Q(v)[t]$ itself. An explicit and elegant formula, as a
polynomial in $t$, of algebraic basis elements is conjectured in [BW13] and
proved in [BeW18]. The purpose of this short paper is to show that the
geometric basis in [LW18] admits the same description and, consequently, that
the two bases coincide.

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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con