scholarly journals TWISTED YANGIANS AND FOLDED ${\mathcal W}$ -ALGEBRAS

2001 ◽  
Vol 16 (13) ◽  
pp. 2411-2433 ◽  
Author(s):  
E. RAGOUCY
Keyword(s):  
Irreducible Representations ◽  
R Matrix ◽  
Finite Dimensional ◽  
Symplectic Algebras

We show that the truncation of twisted Yangians are isomorphic to finite [Formula: see text] -algebras based on orthogonal or symplectic algebras. This isomorphism allows us to classify all the finite-dimensional irreducible representations of the quoted [Formula: see text] -algebras. We also give an R matrix for these [Formula: see text] -algebras, and determine their center.

scholarly journals Representations of Quantum Affine Algebras in their R-Matrix Realization

2020 ◽  
Author(s):  
Naihuan Jing ◽  
◽  
Ming Liu ◽  
Alexander Molev ◽  
◽  
...  
Keyword(s):  
Irreducible Representations ◽  
Quantum Affine Algebras ◽  
R Matrix ◽  
Finite Dimensional ◽  
Gauss Decomposition ◽  
Affine Algebras

We use the isomorphisms between the R-matrix and Drinfeld presentations of the quantum affine algebras in types B, C and D produced in our previous work to describe finite-dimensional irreducible representations in the R-matrix realization.We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the R-matrix and Drinfeld presentations of the Yangians.

scholarly journals GENERALIZED GAUSS DECOMPOSITION OF TRIGONOMETRIC R-MATRICES

1995 ◽  
Vol 10 (19) ◽  
pp. 1375-1392 ◽  
Author(s):  
S.M. KHOROSHKIN ◽  
A.A. STOLIN ◽  
V.N. TOLSTOY
Keyword(s):  
Tensor Product ◽  
Bilinear Form ◽  
Central Charge ◽  
Irreducible Representations ◽  
Verma Modules ◽  
R Matrix ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Gauss Decomposition ◽  
Affine Algebras

The general formula for the universal R-matrix for quantized nontwisted affine algebras, obtained by the first and third authors, is applied to zero central charge, highest weight modules of the quantized affine algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonometric R-matrix in tensor product of these modules. In particular, [Formula: see text] current realization of the universal R-matrix is presented. It gives a new universal presentation for the trigonometric R-matrix with a parameter in tensor product of Uq(sl2)-Verma modules. Detailed analysis of a scalar factor arising in finite-dimensional representations of the universal R-matrix for any Uq(ĝ) is given. We interpret this scalar factor as a multiplicative bilinear form on highest weight polynomials of irreducible representations and express this form in terms of infinite q-shifted factorials.

scholarly journals Description of unitary representations of the group of infinite 𝑝-adic integer matrices

2021 ◽  
Vol 25 (21) ◽  
pp. 606-643
Author(s):  
Yury Neretin
Keyword(s):  
Irreducible Representation ◽  
Unitary Representations ◽  
Irreducible Representations ◽  
Infinite Matrices ◽  
Natural Topology ◽  
Content Type ◽  
Residue Ring ◽  
Finite Dimensional ◽  
Irreducible Unitary Representations

We classify irreducible unitary representations of the group of all infinite matrices over a p p -adic field ( p ≠ 2 p\ne 2 ) with integer elements equipped with a natural topology. Any irreducible representation passes through a group G L GL of infinite matrices over a residue ring modulo p k p^k . Irreducible representations of the latter group are induced from finite-dimensional representations of certain open subgroups.

AN INTEGRABLE DECOMPOSITION OF THE SYMMETRIC MATRIX KdV EQUATION

2008 ◽  
Vol 22 (13) ◽  
pp. 1307-1315
Author(s):  
RUGUANG ZHOU ◽  
ZHENYUN QIN
Keyword(s):  
Hamiltonian Systems ◽  
Matrix Method ◽  
Kdv Equation ◽  
Symmetric Matrix ◽  
Lax Pair ◽  
Integrable Hamiltonian Systems ◽  
R Matrix ◽  
Finite Dimensional ◽  
Higher Rank ◽  
Gaudin Models

A technique for nonlinearization of the Lax pair for the scalar soliton equations in (1+1) dimensions is applied to the symmetric matrix KdV equation. As a result, a pair of finite-dimensional integrable Hamiltonian systems, which are of higher rank generalization of the classic Gaudin models, are obtained. The integrability of the systems are shown by the explicit Lax representations and r-matrix method.

scholarly journals Finite-Dimensional Representations of Yangians in Complex Rank

2019 ◽  
Vol 2020 (20) ◽  
pp. 6967-6998 ◽  
Author(s):  
Daniil Kalinov
Keyword(s):  
Irreducible Representations ◽  
Finite Dimensional

Abstract We classify the “finite-dimensional” irreducible representations of the Yangians $Y(\mathfrak{g}\mathfrak{l}_t)$ and $Y(\mathfrak{s}\mathfrak{l}_t)$. These are associative ind-algebras in the Deligne category $\textrm{Rep}(GL_t)$, which generalize the regular Yangians $Y(\mathfrak{g}\mathfrak{l}_n)$ and $Y(\mathfrak{s}\mathfrak{l}_n)$ to complex rank. They were first defined in the paper [14]. Here we solve [14, Problem 7.2]. We work with the Deligne category $\textrm{Rep}(GL_t)$ using the ultraproduct approach introduced in [7] and [16].

Jacobi–Trudi type formula for a class of irreducible representations of 𝔤𝔩(m|n)

2020 ◽  
pp. 2250015
Author(s):  
Nguyên Luong Thái Bình
Keyword(s):  
Irreducible Representations ◽  
Fundamental Representation ◽  
Symmetric Powers ◽  
Type Formula ◽  
Finite Dimensional

We prove a determinantal type formula to compute the characters of a class of finite-dimensional irreducible representations of the general Lie super-algebra [Formula: see text] in terms of the characters of the symmetric powers of the fundamental representation and their duals. This formula, originally conjectured by van der Jeugt and Moens, can be regarded as a generalization of the well-known Jacobi–Trudi formula.

Note on Weight Spaces of Irreducible Linear Representations

1968 ◽  
Vol 11 (3) ◽  
pp. 399-403 ◽  
Author(s):  
F. W. Lemire
Keyword(s):  
Irreducible Representation ◽  
Weight Function ◽  
Wide Class ◽  
Irreducible Representations ◽  
Weight Space ◽  
Closed Field ◽  
One Dimensional ◽  
Highest Weight ◽  
Linear Representations ◽  
Finite Dimensional

Let L denote a finite dimensional, simple Lie algebra over an algebraically closed field F of characteristic zero. It is well known that every weight space of an irreducible representation (ρ, V) admitting a highest weight function is finite dimensional. In a previous paper [2], we have established the existence of a wide class of irreducible representations which admit a one-dimensional weight space but no highest weight function. In this paper we show that the weight spaces of all such representations are finite dimensional.

Sign in / Sign up

Export Citation Format

Share Document