Related papers: Crystal structure of level zero extremal weight mo…

This work provides the first step toward the classification of irreducible finite weight modules over twisted affine Lie superalgebras. We study all such modules whether the canonical central element acts as a nonzero multiple of the…

We generalize the results of [KMST] concerning equivariant quantization by means of Verma modules $M(\lambda)$ for generic weight $\lambda$ to the case of general $\lambda$. We consider the relationship between the Shapovalov form on an…

Modular symmetries are known to be powerful and have various remarkable properties. We point out that the structure of vector-valued modular forms (VVMFs) space leads to the absence of couplings which cannot be explained in terms of the…

We study the structure of weight modules $V$ with restrictions neither on the dimension nor on the base field, over split Lie algebras $L$. We show that if $L$ is perfect and $V$ satisfies $LV=V$ and ${\mathcal Z}(V)=0$, then $$\hbox{$L…

We want to introduce a construction of spherical designs from finite graphs with the theory of crystal lattice. We start from a finite graph, and we consider standard realization of the crystal lattices as the maximal Abelian covering of…

We study the crystal of quantum nilpotent subalgebra of $U_q(D_n)$ associated to a maximal Levi subalgebra of type $A_{n-1}$. We show that it has an affine crystal structure of type $D_n^{(1)}$ isomorphic to a limit of perfect…

It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T_n theories. The…

We give a new short proof that the wheeled operad of unimodular Lie algebras is Koszul and use this to explicitly construct its minimal resolution. A representation of this resolution in a finite dimensional vector space V we call a…

We study a relationship between the graded characters of generalized Weyl modules $W_{w \lambda}$, $w \in W$, over the positive part of the affine Lie algebra and those of specific quotients $V_{w}^- (\lambda) / X_{w}^- (\lambda)$, $w \in…

The atomic and electronic structure of the p-type transparent amorphous semiconductor CuI is calculated by ab-initio molecular dynamics. It is found to consist of a random tetrahedrally bonded network. The hole effective mass is found to be…

The product monomial crystal was defined by Kamnitzer, Tingley, Webster, Weekes, and Yacobi for any semisimple simply-laced Lie algebra $\mathfrak{g}$, and depends on a collection of parameters $\mathbf{R}$. We show that a family of…

In earlier work with C.~Monical, we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured that such a K-crystal structure existed on the set of…

Let $\fg$ be any untwisted affine Kac-Moody algebra, $\mu$ any fixed complex number, and $\wt\fg(\mu)$ the corresponding toroidal extended affine Lie algebra of nullity two. For any $k$-tuple $\bm{\lambda}=({\lambda}_1, \cdots,…

We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model.…

We deal with finite dimensional differentiable manifolds. All items are concerned with are differentiable as well. The class of differentiability is $C^\infty$. A metric structure in a vector bundle $E$ is a constant rank symmetric bilinear…

Let $\mathfrak{g}$ be a complex Kac-Moody algebra, with Cartan subalgebra $\mathfrak{h}$. Also fix a weight $\lambda\in\mathfrak{h}^*$. For $M(\lambda)\twoheadrightarrow V$ an arbitrary highest weight $\mathfrak{g}$-module, we provide a…

Answering a question of Kuniba, Misra, Okado, Takagi, and Uchiyama, it is shown that certain Demazure characters of affine type A, coincide with the graded characters of coordinate rings of closures of conjugacy classes of nilpotent…

Symmetry equations are obtained for the rigidity matrices associated with various forms of infinitesimal flexibility for an idealised bond-node crystal framework $\C$ in $\bR^d$. These equations are used to derive symmetry-adapted…

We prove the existence of extremal, non-csc, K\"ahler metrics on certain unstable projectivised vector bundles $\P (E) \to M$ over a cscK-manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic K\"ahler classes. In…

For each integral dominant weight $\lambda$, we construct a twisted global section functor $\Gamma^{\lambda}$ from the category of critical twisted $D$-modules on affine Grassmannian to the category of $\lambda$-regular modules of affine…