Related papers: Zero Action on Perfect Crystals for U_q(G_2^{(1)})

We completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A. Kishimoto's result on the simplicity of such crossed products. We also give a…

n this paper I introduce a new description of the crystal $B(\Lambda_0)$ of $\hat{\mathfrak{sl}_\ell}$. As in the Misra-Miwa model of $B(\Lambda_0)$, the nodes of this crystal are indexed by partitions and the $i$-arrows correspond to…

In the recent papers with Masaki Kashiwara, the author introduced the notion of symmetric crystals and presented the Lascoux-Leclerc-Thibon-Ariki type conjectures for the affine Hecke algebras of type $B$. Namely, we conjectured that…

We describe the structure of the free actions of the Klein bottle group by orientation preserving homeomorphisms of the plane. This group is generated by two elements $a,b$, where the conjugate of $b$ by $a$ equals the inverse of $b$. The…

In this letter, we present the first fully analytic derivation and implementation of nuclear gradients for the G$_0$W$_0$ method. For this, we leverage the recently established connection between the G$_0$W$_0$ approach and…

For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect…

We study how the category of $q$-connections depends on the choice of coordinates. We exploit Bhatt's and Scholze's $q$-crystalline site, which is based on a coordinate free formulation of $q$-PD structures, in order to relate $q$-crystals…

Let $G$ be a compact Lie group and $T$ its maximal torus. The composition of maps $ H^*(BG)\to H^*(BT) \to H^*(G/T)$ is zero for positive degree, while it is far from exact. We change $H^*(G/T)$ by Chow ring $CH^*(X)$ for $X$ some twisted…

The exact renormalization group is applied to the world sheet theory describing bosonic open string backgrounds to obtain the equations of motion for the fields of the open string. Using loop variable techniques the equations can be…

In this paper, we introduce a notion of a self-similar action of a group $G$ on a $k$-graph $\Lambda$, and associate it a universal C*-algebra $\O_{G,\Lambda}$. We prove that $\O_{G,\Lambda}$ can be realized as the Cuntz-Pimsner algebra of…

We construct an explicit algorithm of the static-preserving bijection between the rigged configurations and the highest weight paths of the form $(B^{2,1})^{\otimes L}$ in the $G_{2}^{(1)}$ adjoint crystals.

We prove that for any second-countable, locally compact group $G$, any continuous $G$-action on the primitive ideal space of a separable, nuclear $\mathrm{C}^{\ast}$-algebra $B$ such that $B \cong B\otimes\mathcal{K}\otimes\mathcal{O}_2$ is…

We study partial actions of exact discrete groups on C*-algebras. We show that the partial crossed product of a commutative C*-algebra by an exact discrete group is nuclear whenever the full and reduced partial crossed products coincide.…

The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. N\'emeth and M. Challacombe, J. Chem. Phys. {\bf 121}, 2877, (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid…

We consider imaginary Verma modules for quantum affine algebraU_q(\widehat{\mathfrak{sl}(2)}) and define a crystal-like base which we call an imaginary crystal basis using the Kashiwara algebra K_q constructed in earlier work of the…

We apply the method of Hasenfratz and Niedermayer to analytically construct perfect lattice actions for the Gross--Neveu model. In the large $N$ limit these actions display an exactly perfect scaling, i.e. cut-off artifacts are completely…

Let $\mathrm{L}^2_a(\mathbb{D})$ be the classical Bergman space and denote $M_h$ for the multiplication operator by a function $h$. Let $B$ be a finite Blaschke product with order $n$.An open question proposed by R. G. Douglas is whether…

According to the classical theorem, every irreducible algebraic variety endowed with a nontrivial rational action of a connected linear algebraic group is birationally isomorphic to a product of another algebraic variety and ${\bf P}^s$…

We construct an action of a braid group associated to a complete graph on the derived category of a certain symmetric Nakayama algebra which is also a Brauer star algebra with no exceptional vertex. We connect this action with the affine…

We consider reduced imaginary Verma modules for the untwisted quantum affine algebras $U_q(\hat{\g})$ and define a crystal-like base which we call imaginary crystal base using the Kashiwara algebra $\mathcal K_q$ constructed in earlier work…