Related papers: Webs and canonical bases in degree two

This is the second part of the paper devoted to the general proof of canonicity of Baecklund transformation (BT) for a Hamiltonian integrable system governed by SL(2)-invariant r-matrix. Introducing an extended phase space from which the…

In this paper, we study the structures of Schur algebra and Lusztig algebra associated to partial flag varieties of affine type D. We show that there is a subalgebra of Lusztig algebra and the quantum groups arising from this subalgebras…

The spaces of invariants of tensor powers of the defining representation of Sp(2n) are provided with the bases parametrized by symplectic wave graphs introduced here especially for this purpose. The proof utilizes a game similar to Tetris,…

In this article we use the cluster structure on the Grassmannian and the combinatorics of plabic graphs to exhibit a new aspect of mirror symmetry for Grassmannians in terms of polytopes. For our $A$-model, we consider the Grassmannian…

Let $V$ be a two-dimensional vector space over a field $\mathbb F$ of characteristic not $2$ or $3$. We show there is a canonical surjection $\nu$ from the set of suitably generic commutative algebra structures on $V$ modulo the action of…

We give a systematic description of many monomial bases for a given quantized enveloping algebra and of many integral monomial bases for the associated Lusztig $\mathbb Z[v,v^{-1}]$-form. The relations between monomial bases, PBW bases and…

We construct, for q a root of unity of odd order, an embedding of the projective special linear group PSL(n) into the group of bi-Galois objects over u_q(sl(n))*, the coordinate algebra of the Frobenius-Lusztig kernel of SL(n), which is…

In a previous article, a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes. This formalism was…

Semi-log canonical varieties are a higher-dimensional analogue of stable curves. They are the varieties appearing as the boundary $\Delta$ of a log canonical pair $(X,\Delta)$, and also appear as limits of canonically polarized varieties in…

In this paper we determine topologically the canonical component of the $SL_2(\mathbb{C})$ character variety of the Whitehead link complement.

Let $\Sigma_g$ be a closed oriented surface of genus g and let $H_\mathbb{Q}$ denote $H_1(\Sigma_g;\mathbb{Q})$ which we understand to be the standard symplectic vector space over $\mathbb{Q}$ of dimension $2g$. We introduce a canonical…

We define an invariant of Legendrian links in the double-point enhanced grid homology of a link, and prove that it obstructs decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on $\mathbb R^3$.

We give some closed formulas for certain vectors of the canonical bases of the Fock space representation of U_v(sl^_n). As a result, a combinatorial description of certain parabolic Kazhdan-Lusztig polynomials for affine type A is obtained.

We give bounds on the L(2,1)-labeling number of a simple graph in terms of its order and its maximum degree. We also describe an infinite class of graphs of which the elements have the highest L(2,1)-labeling numbers in terms of their…

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$. In the 1950s Chevalley showed that $\mathfrak{g}$ admits particular bases, now called ``Chevalley bases'', for which the corresponding structure constants are…

We investigate holomorphic webs tangent to real-analytic Levi-flat hypersurfaces on compact complex surfaces. Under certain conditions, we prove that a holomorphic web tangent to a real-analytic Levi-flat hypersurface admits a…

Let F be a totally real Galois number field. We prove the existence of base change relative to the extension F/Q for every classical newform of odd level, under simple local assumptions on the field F.

Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as sl(2,C)-modules. As finite-dimensional irreducible sl(2,C)-modules, they have canonical bases which are, by construction, orthogonal. In this note, we…

We show that every canonical Seifert surface is (up to isotopy) given by a knot diagram in which the (open) Seifert disks are pairwise disjoint.

We consider any classical Grassmannian geometry $\Gamma$; that is, any projective or polar Grassmann space. Suppose every line in $\Gamma$ contains $s+1$ points. Then we classify all sets of points in $\Gamma$ of cardinality $s+1$, with the…