相关论文: A bijection between type D_n^{(1)} crystals and ri…

A method to calculate matrix representations of the twist element $\ff$ of Drinfel'd -- chosen to be unitary -- is given and illustrated at some examples. It is observed that for these F-matrices the crystal limit $q\!\to\! 0$ exists and…

Analytic Bethe ansatz is executed for a wide class of finite dimensional $U_q(B^{(1)}_r)$ modules. They are labeled by skew-Young diagrams which, in general, contain a fragment corresponding to the spin representation. For the transfer…

We propose to generalize Benkart-Frenkel-Kang-Lee's adjoint crystals and describe their crystal structure for type $A\sb{n}\sp{(1)}$, $C\sb{n}\sp{(1)}$ and $D\sb{n+1}\sp{(2)}$.

We give a geometric model for the non-$\tau$-rigid modules over acyclic path algebras of type $\widetilde{D}_n$. Similar models have been provided for module categories over path algebras of types $A_n, D_n,$ and $\widetilde{A}_n$ as well…

We present a simple bijection between restricted (Bressoud) lattice paths and RSOS paths in regime II. Both types of paths describe states in Z_k parafermionic irreducible modules. The bijection implies a direct correspondence between a…

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be…

A di-sk tree is a rooted binary tree whose nodes are labeled by $\oplus$ or $\ominus$, and no node has the same label as its right child. The di-sk trees are in natural bijection with separable permutations. We construct a combinatorial…

For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver…

We define a bijection that transforms an alternating sign matrix A with one -1 into a pair (N,E) where N is a (so called) ``neutral'' alternating sign matrix (with one -1) and E is an integer. The bijection preserves the classical…

We study the path realization of Demazure crystals related to solvable lattice models in statistical mechanics. Various characters are represented in a unified way as the sums over one dimensional configurations which we call unrestricted,…

We give a new model for the crystal graphs of an affine Lie algebra g^, combining Littelmann's path model with the Kyoto path model. The vertices of the crystal graph are represented by certain infinitely looping paths which we call skeins.…

Dual formulations of Abelian U(1) and Z(N) LGT with a static fermion determinant are constructed at finite temperatures and non-zero chemical potential. The dual form is valid for a broad class of lattice gauge actions, for arbitrary number…

We present a list of ``local'' axioms and an explicit combinatorial construction for the regular $B_2$-crystals (crystal graphs of highest weight integrable modules over $U_q(sp_4)$). Also a new combinatorial model for these crystals is…

Let G be a connected split reductive group over a complete discrete valuation ring of mixed characteristic. We use the theory of intermediate extensions due to Abe-Caro and arithmetic Beilinson-Bernstein localization to classify irreducible…

In the previous paper "Symmetric Crystals and Affine Hecke Algebras of Type B", we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for…

We review the numerical analysis' understanding of Krylov subspace methods for solving (non-hermitian) systems of equations and discuss its implications for lattice gauge theory computations using the example of the Wilson fermion matrix.…

We define three combinatorial models for \hat{sl(n)} crystals, parametrized by partitions, configurations of beads on an `abacus', and cylindric plane partitions, respectively. These are reducible, but we can identify an irreducible…

Regular $A_n$-crystals are certain edge-colored directed graphs which are related to representations of the quantized universal enveloping algebra $U_q(\mathfrak{sl}_{n+1})$. For such a crystal $K$ with colors $1,2,...,n$, we consider its…

In this paper, we recall Lepowsky's and Wakimoto's product character formulas formulated in a new way by using arrays of specialized weighted crystals of negative roots for affine Lie algebras of type $C_l^{(1)}$, $D_{l+1}^{(2)}$ and…

The alcove model of the first author and A. Postnikov uniformly describes highest weight crystals of semisimple Lie algebras. We construct a generalization, called the quantum alcove model. In joint work of the first author with S. Naito,…