Related papers: Notes on affine canonical and monomial bases

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.

Affine structures on a Lie groupoid, including affine $k$-vector fields, $k$-forms and $(p,q)$-tensors are studied. We show that the space of affine structures is a 2-vector space over the space of multiplicative structures. Moreover, the…

We establish a connection between (degenerate) nonsymmetric Macdonald polynomials and standard bases and dual standard bases of maximal parabolic modules of affine Hecke algebras. Along the way we prove a (weak) polynomiality result for…

Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of basis for morphisms of matroids, and show that its generating function is strongly log-concave. As a consequence, we…

We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…

Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of…

We construct a gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition at a rigid, regular, codimension one configuration. This construction plays an important role in establishing the relation…

A good canonical projection of a surface $S$ of general type is a morphism to the 3-dimensional projective space P^3 given by 4 sections of the canonical line bundle. To such a projection one associates the direct image sheaf F of the…

We identify the dominant part of the Frenkel-Reshetikhin $q$-character with a natural invariant arising from the Langlands/Zelevinsky parameterization for affine Hecke algebras. We introduce the reciprocal character of a module over a…

This paper is concerned with one-dimensional sums in classical affine types. We prove a conjecture of the third author and Zabrocki by showing they all decompose in terms of one-dimensional sums related to affine type A provided the rank of…

We compute the diagonal F-thresholds of determinantal hypersurfaces arising from a generic matrix and from a generic symmetric matrix, as well as of the Pfaffian hypersurface arising from a generic skew-symmetric matrix of even size. The…

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…

Let I be a finite set and CI be the algebra of functions on I. For a finite dimensional C algebra A with \CI contained in A we show that certain moduli spaces of finite dimsional modules are isomorphic to certain Grassmannian (quot-type)…

Shafarevich's hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by…

In this paper, we study the dependence of the weak Lefschetz property of algebras defined by a special class of monomials ideals in a polynomial ring with coefficient in a field, to the characteristic of the base field.

We show the positivity of the canonical basis for a modified quantum affine $\mathfrak{sl}_n$ under the comultiplication. Moreover, we establish the positivity of the i-canonical basis in [LW15] with respect to the coideal subalgebra…

We prove a conjecture of Kashiwara and Miemietz on canonical bases and branching rules of affine Hecke algebras of type D. The proof is similar to the proof of the type B case.

In this article we present the basis of Monoid Theory from a categorical point of view, emphasizing the analogies and differences between the theory of modules over commutative rings. We present the generalization of afine schemes and afine…

Let $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V \to V$ and $A^*:V \to V$ that satisfy (i), (ii) below: (i) There exists a basis for $V$…

We first obtain the most general and compact parametrization of the unitary transformation diagonalizing any 3 by 3 hermitian matrix H, as a function of its elements and eigenvalues. We then study a special class of fermion mass matrices,…