اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPrincipal Realization of the Yangian Y(gl(n))
102
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian $Y(sl(n))$ using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard Cartan-Weyl basis is also given. We show by example that the principal basis simplifies the Yangian action significantly in the tensor product of the fundamental representation and its dual.
قيم البحث
اقرأ أيضاً
We show that the Kazhdan-Lusztig category $KL_k$ of level-$k$ finite-length modules with highest-weight composition factors for the affine Lie superalgebra $widehat{mathfrak{gl}(1|1)}$ has vertex algebraic braided tensor supercategory structure, and
that its full subcategory $mathcal{O}_k^{fin}$ of objects with semisimple Cartan subalgebra actions is a tensor subcategory. We show that every simple $widehat{mathfrak{gl}(1|1)}$-module in $KL_k$ has a projective cover in $mathcal{O}_k^{fin}$, and we determine all fusion rules involving simple and projective objects in $mathcal{O}_k^{fin}$. Then using Knizhnik-Zamolodchikov equations, we prove that $KL_k$ and $mathcal{O}_k^{fin}$ are rigid. As an application of the tensor supercategory structure on $mathcal{O}_k^{fin}$, we study certain module categories for the affine Lie superalgebra $widehat{mathfrak{sl}(2|1)}$ at levels $1$ and $-frac{1}{2}$. In particular, we obtain a tensor category of $widehat{mathfrak{sl}(2|1)}$-modules at level $-frac{1}{2}$ that includes relaxed highest-weight modules and their images under spectral flow.
For the quantum algebra U_q(gl(n+1)) in its reduction on the subalgebra U_q(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction Z-algebra Z_q(gl(n+1),gl(n)) is given in terms of the generators and their defining relations. Using this
Z-algebra we describe Hermitian irreducible representations of a discrete series for the noncompact quantum algebra U_q(u(n,1)) which is a real form of U_q(gl(n+1)), namely, an orthonormal Gelfand-Graev basis is constructed in an explicit form.
Let $mathsf k$ be a local field. Let $I_ u$ and $I_{ u}$ be smooth principal series representations of $mathrm{GL}_n(mathsf k)$ and $mathrm{GL}_{n-1}(mathsf k)$ respectively. The Rankin-Selberg integrals yield a continuous bilinear map $I_ utimes I_{
u}rightarrow mathbb C$ with a certain invariance property. We study integrals over a certain open orbit that also yield a continuous bilinear map $I_ utimes I_{ u}rightarrow mathbb C$ with the same invariance property, and show that these integrals equal the Rankin-Selberg integrals up to an explicit constant. Similar results are also obtained for Rankin-Selberg integrals for $mathrm{GL}_n(mathsf k)times mathrm{GL}_n(mathsf k)$.
We construct an analog of the subalgebra $Ugl(n)otimes Ugl(m)$ of $Ugl(m+n)$ in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.
In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F. We study r
educibility and composition series of such representations. Similar results were obtained already in [HL99,Al12,Zel80], but we give a short uniform proof in the general case, using the tools from [AGS15a]. We also indicate some applications to cosine transforms in integral geometry.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
