Completely splittable representations of affine Hecke-Clifford algebras

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.Comment: 39 pages, v2, added a new reference with comments in section 4.4, added two examples (Example 5.4 and Example 5.11) in section 5, mild corrections of some typos, to appear in J. Algebraic Combinatoric

Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A

We are interested in the structure of the crystal graph of level $l$ Fock spaces representations of $\mathcal{U}_q (\widehat{\mathfrak{sl}_e})$. Since the work of Shan [26], we know that this graph encodes the modular branching rule for a corresponding cyclotomic rational Cherednik algebra. Besides, it appears to be closely related to the Harish-Chandra branching graph for the appropriate finite unitary group, according to [8]. In this paper, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces. This so-called "canonical" crystal isomorphism turns out to be expressible only in terms of: - Schensted's classic bumping procedure, - the cyclage isomorphism defined in [13], - a new crystal isomorphism, easy to describe, acting on cylindric multipartitions. We explain how this can be seen as an analogue of the bumping algorithm for affine type $A$. Moreover, it yields a combinatorial characterisation of the vertices of any connected component of the crystal of the Fock space

Non-uniqueness of the Dirac theory in a curved spacetime

We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. In this paper, we focus on the standard version of the gravitational Dirac equation, but the non-uniqueness applies also to our alternative versions. We find that the changes which lead to an equivalent operator H, or respectively to an equivalent operator E, are determined by initial data, or respectively have to make some point-dependent antihermitian matrix vanish. Thus, the vast majority of the possible coefficient changes lead neither to an equivalent operator H, nor to an equivalent operator E, whence a lack of uniqueness. We show that even the Dirac energy spectrum is not unique.Comment: 13 pages (standard 12pt article format). Text of a talk given at the 1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbari (Greece), Sept. 14-18, 200

On irreducibility of tensor products of evaluation modules for the quantum affine algebra

Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules.Comment: 22 pages. Some references are adde

Vertical sleeve gastrectomy lowers SGLT2/Slc5a2 expression in the mouse kidney

Bariatric surgery improves glucose homeostasis but the underlying mechanisms are not fully elucidated. Here, we show that the expression of sodium glucose cotransporter-2 (SGLT2/Slc5a2) is reduced in the kidney of lean and obese mice following vertical sleeve gastrectomy (VSG). Indicating an important contribution of altered cotransporter expression to the impact of surgery, inactivation of the SGLT2/Slc5a2 gene by CRISPR/Cas9 attenuated the effects of VSG, with glucose excursions following intraperitoneal injection lowered by ∼30% in wild-type mice but by ∼20% in SGLT2 null animals. The effects of the SGLT2 inhibitor dapaglifozin were similarly blunted by surgery. Unexpectedly, effects of dapaglifozin were still observed in SGLT2 null mice, consistent with the existence of metabolically beneficial off-target effects of SGLT2 inhibitors. Thus, we describe a new mechanism involved in mediating the glucose lowering effects of bariatric surgery

Fermionic realization of two-parameter quantum affine algebra Ur,s(sln)U_{r,s}({sl_n})

We construct all fundamental modules for the two parameter quantum affine algebra of type $A$ using a combinatorial model of Young diagrams. In particular we also give a fermionic realization of the two-parameter quantum affine algebra

DIFFICULTÉS DE LA PARTICIPATION EN RECHERCHE- ACTION : retour d'expériences de modélisation d'accompagnement en appui à l'aménagement du territoire au Sénégal et à la Réunion

International audienceComment aider les institutions et acteurs locaux à investir davantage les processus d'affectation des terres pour aménager leur territoire ? La décentralisation de l'aménagement du territoire engagée à la Réunion et au Sénégal est inachevée. Malgré l'arsenal législatif, les populations locales semblent peu impliquées dans les décisions les concernant en raison notamment de la difficulté à appréhender la complexité des systèmes d'interactions entre dynamiques sociales et environnementales. Le projet Domino vise à accompagner les processus de décision en proposant aux acteurs de construire et d'explorer des scenarii prospectifs d'affectation des terres. Cette expérience de modélisation participative repose sur une dynamique partenariale complexe sur chaque terrain, source de difficultés. Conscients des dérives potentielles, nous discutons la nécessité de construire une démarche qualité de notre recherche-action. Mots clés : montage de partenariat, démarche qualité, modèle, changement social, ComMod, interdisciplinarité, décentralisation, foncier, Sénégal, Réunio

Shot Noise in Digital Holography

We discuss on noise in heterodyne holography in an off-axis configuration. We show that, for a weak signal, the noise is dominated by the shot noise on the reference beam. This noise corresponds to an equivalent noise on the signal beam of one photoelectron per pixel, for the whole sequence of images used to build the digital hologram

Decreased STARD10 expression is associated with defective insulin secretion in humans and mice

Genetic variants near ARAP1 (CENTD2) and STARD10 influence type 2 diabetes (T2D) risk. The risk alleles impair glucose-induced insulin secretion and, paradoxically but characteristically, are associated with decreased proinsulin:insulin ratios, indicating improved proinsulin conversion. Neither the identity of the causal variants nor the gene(s) through which risk is conferred have been firmly established. Whereas ARAP1 encodes a GTPase activating protein, STARD10 is a member of the steroidogenic acute regulatory protein (StAR)-related lipid transfer protein family. By integrating genetic fine-mapping and epigenomic annotation data and performing promoter-reporter and chromatin conformational capture (3C) studies in β cell lines, we localize the causal variant(s) at this locus to a 5 kb region that overlaps a stretch-enhancer active in islets. This region contains several highly correlated T2D-risk variants, including the rs140130268 indel. Expression QTL analysis of islet transcriptomes from three independent subject groups demonstrated that T2D-risk allele carriers displayed reduced levels of STARD10 mRNA, with no concomitant change in ARAP1 mRNA levels. Correspondingly, β-cell-selective deletion of StarD10 in mice led to impaired glucose-stimulated Ca2+ dynamics and insulin secretion and recapitulated the pattern of improved proinsulin processing observed at the human GWAS signal. Conversely, overexpression of StarD10 in the adult β cell improved glucose tolerance in high fat-fed animals. In contrast, manipulation of Arap1 in β cells had no impact on insulin secretion or proinsulin conversion in mice. This convergence of human and murine data provides compelling evidence that the T2D risk associated with variation at this locus is mediated through reduction in STARD10 expression in the β cell

The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $\sigma_{via}$, yields a viable organism with first order growth rate constant $k > 1$ if it is equal to some target ``master'' sequence $\sigma_{via, 0}$. The second gene, denoted by $\sigma_{rep}$, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $\sigma_{rep, 0}$. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on \mu \equiv L\eps , the product of sequence length and per base pair replication error probability, and \eps_r , the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As \eps_r exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds \ln k/\eps_r , while above the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds $\ln k/f_{del}$, where $f_{del}$ denotes the fraction of deleterious mutations.Comment: 14 pages, 3 figures. Submitted to Physical Review