107,446 research outputs found
Coxeter categories and quantum groups
No full textWe define the notion of braided Coxeter category, which is informally a monoidal category carrying compatible, commuting actions of a generalised braid group B_W and Artin’s braid groups B_n on the tensor powers of its objects. The data which defines the action of B_W bears a formal similarity to the associativity constraints in a monoidal category, but is related to the coherence of a family of fiber functors. We show that the quantum Weyl group operators of a quantised Kac–Moody algebra U_{\hbar }{{\mathfrak {g}}}, together with the universal R-matrices of its Levi subalgebras, give rise to a braided Coxeter category structure on integrable, category {\mathcal {O}}-modules for U_{\hbar }{{\mathfrak {g}}}. By relying on the 2-categorical extension of Etingof–Kazhdan quantisation obtained in Appel and Toledano Laredo (Selecta Math NS 24:3529–3617, 2018), we then prove that this structure can be transferred to integrable, category {\mathcal {O}}-representations of {\mathfrak {g}}. These results are used in Appel and Toledano Laredo (arXiv:1512.03041, p 48, 2015) to give a monodromic description of the quantum Weyl group operators of U_{\hbar }{{\mathfrak {g}}}, which extends the one obtained by the second author for a semisimple Lie algebra
Uniqueness of Coxeter structures on Kac–Moody algebras
No full textAbstract. Let g be a symmetrisable Kac–Moody algebra, and Ung the corresponding quantum group. We showed in [1, 2] that the braided Coxeter structure on integrable, category O representations of Ung which underlies the R–matrix actions arising from the Levi subalgebras of Ung and the quantum Weyl group action of the generalised braid group Bg can be transferred to integrable, category O representations of g. We prove in this paper that, up to unique equivalence, there is a unique such structure on the latter category with prescribed restriction functors, R–matrices, and local monodromies. This extends, simplifies and strengthens a similar result of the second author valid when g is semisimple, and is used in [3] to describe the monodromy of the rational Casimir connection of g in terms of the quantum Weyl group operators of Ung. Our main tool is a refinement of Enriquez’s universal algebras, which is adapted to the PROP describing a Lie bialgebra graded by the non–negative roots of g.<br/
Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra
No full textLet g be a symmetrisable Kac-Moody algebra and V an integrable g-module in
category O. We show that the monodromy of the (normally ordered) rational
Casimir connection on V can be made equivariant with respect to the Weyl group
W of g, and therefore defines an action of the braid group B_W of W on V. We
then prove that this action is canonically equivalent to the quantum Weyl group
action of B_W on a quantum deformation of V, that is an integrable, category
O-module V_h over the quantum group U_h(g) such that V_h/hV_h is isomorphic to
V. This extends a result of the second author which is valid for g semisimple.Comment: Some details added. Minor revisions throughout. Published version.
107 page
Appel à contributions - « Cahiers J.-M. G. Le Clézio »
No full textLes Cahiers J.-M. G. Le Clézio, numéro 12 : « Corps » Appel à contributions ci-joint. Date-limite : 31 octobre 2017. Coordinateurs : Justine Feyereisen (Université Libre de Bruxelles) et Paul Dirkx (Université de Lorraine) URL de référence : http://www.associationleclezio.com/activites/les-cahiers-j-m-g-le-clezio Argumentair
An explicit isomorphism between quantum and classical sl(n)
No full textLet g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In this paper we construct explicitly such an isomorphism when g = sl(n), previously known only for n=2
Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
No full textLet be a complex simple Lie algebra and the
corresponding quantum affine algebra. We construct a functor between finite-dimensional modules over a quantum symmetric pair of affine
type and an orientifold KLR algebra
arising from a framed quiver with a contravariant involution, providing a
boundary analogue of Kang-Kashiwara-Kim-Oh generalized Schur-Weyl duality. With
respect to their construction, our combinatorial model is further enriched with
the poles of a trigonometric K-matrix intertwining the action of
on finite-dimensional -modules. By
construction, is naturally compatible with the
Kang-Kashiwara-Kim-Oh functor in that, while the latter is a functor of
monoidal categories, is a functor of module categories.
Relying on a suitable isomorphism \`a la Brundan-Kleshchev-Rouquier, we prove
that recovers the Schur-Weyl dualities due to
Fan-Lai-Li-Luo-Wang-Watanabe in quasi-split type .Comment: Final version. Substantial revision: new examples of enhanced
J-quivers of Dynkin type have been added in Section 6; the material of the
former Sections 6,7, and 11 from v2 has been removed and it will be included
in a separate paper. 50 page
Appel en faveur de la Croix-Rouge suisse et lettre de M. G. Moynier
No full textNous reproduisons ici un appel émané de la Société centrale suisse et que les journaux quotidiens ont publié dernièrement. Cet appel a provoqué de la part de M. G. Moynier quelquesréflexions, qui ont été envoyées au Journal de Genève. Nos lecteurs les trouveront ci-dessou
Integrating the SWAP and Rorschach composite measures for exploring psychopathological patterns of mental functioning
No full textThis study addressed the exploration of a multimethod psychodynamic assessment and its relation to psychopathological patterns. The study applies the Shedler-Westen Assessment Procedure (SWAP; Shedler, J., & Westen, D., 2006, Personality diagnosis with Shedler-Westen Assessment Procedure (SWAP): Bridging the gulf between science and practice. In P. D. M. Task Force (Ed.), Psychodynamic Diagnostic Manual (pp. 573–613). Silver Spring, MD: Alliance of Psychoanalytic Organizations.) and three composite Rorschach measures to a sample of 72 outpatients with various Diagnostic and Statistical Manual of Mental Disorders Axis I diagnoses (American Psychiatric Association, 2000, Diagnostic and Statistical Manual of Mental Disorders (DSM–IV–TR). Washington, DC: Author.): The Ego Impairment Index (EII-2; Viglione, D. J., Perry, W., & Meyer, G. J., 2003, Refinements in the Rorschach Ego Impairment Index incorporating the Human Representational Variable. Journal of Personality Assessment, 81, 149–156. doi:10.1207/S15327752JPA8102_06), measuring maladaptive ego functions; and two derivations of the Reality-Fantasy Scale (RFS; Tibon, S., Handelzalts, J. E., & Weinberger, Y., 2005. Using the Rorschach for exploring the concept of transitional space within the political context of the Middle East. International Journal of Applied Psychoanalytic Studies, 2, 40–57. doi:10.1002/aps.30): the RFS-P, measuring proneness to fantasy (lowered negative scores) as compared to concrete thinking (elevated positive scores); and the RFS-S, measuring dissociative proneness. Consistent with the literature, in this study, the multimethod assessment revealed modest unilinear associations, if any, between each of the Rorschach indices and the SWAP scales. However, regression analyses showed that the joint use of the EII-2 and the RFS-P explained a substantial portion of the variance in the SWAP scales that indicate inhibition and avoidance (obsessive personality disorder score and Avoidant Q factor, respectively). Furthermore, when used with the RFS-S, the EII-2 was able to significantly explain variance in the SWAP scales that indicate interpersonal detachment (schizotypal personality disorder score and Schizoid Q factor). The implications of these results for clinical practice will be discussed
Appel aux Mexicanistes
No full textCallegari G. V. Appel aux Mexicanistes. In: Journal de la Société des Américanistes. Tome 10 n°2, 1913. p. 707
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