اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSimple modules for quiver Hecke algebras and the Robinson-Schensted-Knuth correspondence
221
0
0.0
(
0
)
تأليف
Maxim Gurevich
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We formalize some known categorical equivalences to give a rigorous treatment of smooth representations of p-adic general linear groups, as ungraded modules over quiver Hecke algebras of type A. Graded variants of RSK-standard modules are constructed for quiver Hecke algebras. Exporting recent results from the p-adic setting, we describe an effective method for construction and classification of all simple modules as quotients of modules induced from maximal homogenous data. It is established that the products involved in the RSK construction fit the Kashiwara-Kim notion of normal sequences of real modules. We deduce that RSK-standard modules have simple heads, devise a formula for the shift of grading between RSK-standard and simple self-dual modules, and establish properties of their decomposition matrix, thus confirming expectations for p-adic groups raised in a work of the author with Lapid. Subsequent work will exhibit how the presently introduced RSK construction generalizes the much-studied Specht construction, when inflated from cyclotomic quotient algebras.
قيم البحث
اقرأ أيضاً
We provide the localization procedure for monoidal categories by a real commuting family of braiders. For an element $w$ of the Weyl group, $mathscr{C}_w$ is a subcategory of modules over quiver Hecke algebra which categorifies the quantum unipotent
coordinate algebra $A_q[mathfrak{n}(w)]$. We construct the localization $widetilde{mathscr{C}_w}$ of $mathscr{C}_w$ by adding the inverses of simple modules which correspond to the frozen variables in the quantum cluster algebra $A_q[mathfrak{n}(w)]$. The localization $widetilde{mathscr{C}_w}$ is left rigid and we expect that it is rigid.
By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various combinatorial algorithms, including the RSK correspondence.
We also investigate birational Weyl group actions related to those algorithms.
Let $U_q(mathfrak{g})$ be a twisted affine quantum group of type $A_{N}^{(2)}$ or $D_{N}^{(2)}$ and let $mathfrak{g}_{0}$ be the finite-dimensional simple Lie algebra of type $A_{N}$ or $D_{N}$. For a Dynkin quiver of type $mathfrak{g}_{0}$, we defin
e a full subcategory ${mathcal C}_{Q}^{(2)}$ of the category of finite-dimensional integrable $U_q(mathfrak{g})$-modules, a twisted version of the category ${mathcal C}_{Q}$ introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur-Weyl duality, we construct an exact faithful KLR-type duality functor ${mathcal F}_{Q}^{(2)}: Rep(R) rightarrow {mathcal C}_{Q}^{(2)}$, where $Rep(R)$ is the category of finite-dimensional modules over the quiver Hecke algebra $R$ of type $mathfrak{g}_{0}$ with nilpotent actions of the generators $x_k$. We show that ${mathcal F}_{Q}^{(2)}$ sends any simple object to a simple object and induces a ring isomorphism $K(Rep(R)) simeq K({mathcal C}_{Q}^{(2)})$.
Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the centers. W
e further develop connections of these algebras with the usual degenerate (i.e. graded) affine Hecke algebras of Lusztig by introducing a notion of degenerate covering affine Hecke algebras.
The notion of rational spin double affine Hecke algebras (sDaHa) and rational double affine Hecke-Clifford algebras (DaHCa) associated to classical Weyl groups are introduced. The basic properties of these algebras such as the PBW basis and Dunkl ope
rator representations are established. An algebra isomorphism relating the rational DaHCa to the rational sDaHa is obtained. We further develop a link between the usual rational Cherednik algebra and the rational sDaHa by introducing a notion of rational covering double affine Hecke algebras.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
