اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMinimal affinizations as projective objects
266
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove that the specialization to q=1 of a Kirillov-Reshetikhin module for an untwisted quantum affine algebra of classical type is projective in a suitable category. This yields a uniform character formula for the Kirillov-Reshetikhin modules. We conjecture that these results holds for specializations of minimal affinization with some restriction on the corresponding highest weight. We discuss the connection with the conjecture of Nakai and Nakanishi on q-characters of minimal affinizations. We establish this conjecture in some special cases. This also leads us to conjecture an alternating sum formula for Jacobi-Trudi determinants.
قيم البحث
اقرأ أيضاً
The filtration of the Virasoro minimal series representations M^{(p,p)}_{r,s} induced by the (1,3)-primary field $phi_{1,3}(z)$ is studied. For 1< p/p< 2, a conjectural basis of M^{(p,p)}_{r,s} compatible with the filtration is given by using monomia
l vectors in terms of the Fourier coefficients of $phi_{1,3}(z)$. In support of this conjecture, we give two results. First, we establish the equality of the character of the conjectural basis vectors with the character of the whole representation space. Second, for the unitary series (p=p+1), we establish for each $m$ the equality between the character of the degree $m$ monomial basis and the character of the degree $m$ component in the associated graded module Gr(M^{(p,p+1)}_{r,s}) with respect to the filtration defined by $phi_{1,3}(z)$.
We introduce and define the quantum affine $(m|n)$-superspace (or say quantum Manin superspace) $A_q^{m|n}$ and its dual object, the quantum Grassmann superalgebra $Omega_q(m|n)$. Correspondingly, a quantum Weyl algebra $mathcal W_q(2(m|n))$ of $(m|n
)$-type is introduced as the quantum differential operators (QDO for short) algebra $textrm{Diff}_q(Omega_q)$ defined over $Omega_q(m|n)$, which is a smash product of the quantum differential Hopf algebra $mathfrak D_q(m|n)$ (isomorphic to the bosonization of the quantum Manin superspace) and the quantum Grassmann superalgebra $Omega_q(m|n)$. An interested point of this approach here is that even though $mathcal W_q(2(m|n))$ itself is in general no longer a Hopf algebra, so are some interesting sub-quotients existed inside. This point of view gives us one of main expected results, that is, the quantum (restricted) Grassmann superalgebra $Omega_q$ is made into the $mathcal U_q(mathfrak g)$-module (super)algebra structure,$Omega_q=Omega_q(m|n)$ for $q$ generic, or $Omega_q(m|n, bold 1)$ for $q$ root of unity, and $mathfrak g=mathfrak{gl}(m|n)$ or $mathfrak {sl}(m|n)$, the general or special linear Lie superalgebra. This QDO approach provides us with explicit realization models for some simple $mathcal U_q(mathfrak g)$-modules, together with the concrete information on their dimensions. Similar results hold for the quantum dual Grassmann superalgebra $Omega_q^!$ as $mathcal U_q(mathfrak g)$-module algebra.In the paper some examples of pointed Hopf algebras can arise from the QDOs, whose idea is an expansion of the spirit noted by Manin in cite{Ma}, & cite{Ma1}.
Given an orthogonal compact matrix quantum group defined by intertwiner relations, we characterize by relations its projective version. As a sample application, we prove that $PU_n^+=PO_n^+$. We also give a combinatorial proof of the fact that $S_{n^2}^+$ is monoidally equivalent to $PO_n^+$.
We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi--Yau algebras that serve as their homogeneous coordinate rings. We prove that the space parametrizing such deformations has exactly six ir
reducible components, and we give explicit presentations for the generic members of each family in terms of generators and relations. The proof uses deformation quantization to reduce the problem to a similar classification of unimodular quadratic Poisson structures in four dimensions, which we extract from Cerveau and Lins Netos classification of degree-two foliations on projective space. Corresponding to the ``exceptional component in their classification is a quantization of the third symmetric power of the projective line that supports bimodule quantizations of the classical Schwarzenberger bundles.
We show various properties of smooth projective D-affine varieties. In particular, any smooth projective D-affine variety is algebraically simply connected and its image under a fibration is D-affine. In characteristic zero such D-affine varieties ar
e also uniruled. We also show that (apart from a few small characteristics) a smooth projective surface is D-affine if and only if it is isomorphic to either ${mathbb P}^2$ or ${mathbb P}^1times {mathbb P}^1$. In positive characteristic, a basic tool in the proof is a new generalization of Miyaokas generic semipositivity theorem.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
