Related papers: Descriptions of the crystal $B(\infty)$ for $G_2$
Let K be a finite unramified extension of Q_p. We parametrize the (phi, Gamma)-modules corresponding to reducible two-dimensional mod p representations of G_K and characterize those which have reducible crystalline lifts with certain…
For a group $G$, a weak Cayley isomorphism is a bijection $f:G \to G$ such that $f(g_1g_2)$ is conjugate to $ f(g_1)f(g_2)$ for all $g_1,g_2 \in G$. They form a group $\mathcal W(G)$ that is the group of symmetries of the weak Cayley table…
This paper gives a characterisation of the group G_2(K) over an algebraically closed field K of characteristic not 2 inside the class of simple K*-groups of finite Morley rank not interpreting a bad field using the structure of centralizers…
The current status of some methods to determine the weak phase $\gamma$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V^*_{ub}$ using B decays is discussed, and comments are made on accuracy achievable in the next few years.
The temperature dependence of the London penetration depth ($\lambda$) and coherence length ($\xi$) has been deduced from Hall probe magnetization measurements in high quality MgB$_2$ single crystals in the two main crystallographic…
Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the…
By utilizing the combinatorial properties of various tableau models, we establish an explicit correspondence between the polyhedral realizations of the crystal bases $\mathcal B(\lambda)$ (resp. $\mathcal B(\infty)$) of type $A_n$ and the…
We portray the structure of quantum gravity emerging from recent progress in understanding the quantum mechanics of an evaporating black hole. Quantum gravity admits two different descriptions, based on Euclidean gravitational path integral…
Tsuzuki has conjectured that for crystals with Frobenius and connection over a local field k((t)), the embedding of the category of overconvergent crystals into the category of convergent crystals is fully faithful. We prove Tsuzuki's…
Quantization of gravitational field in the neighbourhood of exact solution of Einstein equation is considered. The method of Bogoliubov group variables is used.
In general, ring theory is focused on atomic rings, i.e. rings in which every element has some factorization into irreducible elements. In a recent paper of Boynton and Coykendall \cite{BC}, the two authors introduce two properties that are…
We show that the rigid C*-tensor categories of finite dimensional type 1 unitary representations of the quantum groups $U_{q}(\mathfrak{g}_{2})$ corresponding to the exceptional Lie group $G_2$ for positive $q\ne 1$ have property (T).
We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics, the other from gauge theory. We show that the two are governed by the same combinatorics and therefore…
We introduce the notion of a crystal base of a finite dimensional q-deformed Kac module over the quantum superalgebra $U_q(\gl(m|n))$, and prove its existence and uniqueness. In particular, we obtain the crystal base of a finite dimensional…
We investigate the finite groups $G$ for which $\chi(1)^{2}=|G:Z(\chi)|$ for all characters $\chi \in Irr(G)$ and $|cd(G)|=2$. We obtain some alternate characterizations of these groups and we obtain some information regarding the structure…
In this paper, we develop the crystal basis theory for quantum generalized Kac-Moody algebras. For a quantum generalized Kac-Moody algebra $U_q(\mathfrak g)$, we first introduce the category $\mathcal O_{int}$ of $U_q(\mathfrak g)$-modules…
If G is a finite group, we have proposed new conjectures on the interaction between different primes and their corresponding Brauer principal blocks. In this paper, we give strong support to the validity of these conjectures.
The structure of quantum principal bundles is studied, from the viewpoint of Tannaka-Krein duality theory. It is shown that if the structure quantum group is compact, principal G-bundles over a quantum space M are in a natural…
We present diagonal and off-diagonal elements of the permittivity and conductivity tensor up to the second order in magnetization for cubic crystals. We express all tensor elements as a function of a general sample orientation, for…
In this report we present the detail theory of the focusing in bent crystals using the statistical mechanics. The quantum mechanical effects for focusing and abberations are not considered. The beam structure in phase space are consedered…