68 citations · 189 across the 17 of their papers we have counts for
17 papers
On the uniqueness of Yangians
Sachin Gautam, Curtis Wendlandt, Siwei Xu
Let be a simple Lie algebra over the complex numbers, and let denote its polynomial current algebra. In the mid-1980s, Drinfeld introduced the Yang…
Braid group actions, Baxter polynomials, and affine quantum groups
Noah Friesen, Alex Weekes, Curtis Wendlandt
It is a classical result in representation theory that the braid group of a simple Lie algebra acts on any integrable representation of $\…
The R-matrix of the affine Yangian
Andrea Appel, Sachin Gautam, Curtis Wendlandt
Let g be an affine Lie algebra with associated Yangian Y_hg. We prove the existence of two meromorphic R-matrices associated to any pair of representations of Y_hg in the category…
The R-matrix presentation for the rational form of a quantized enveloping algebra
Matthew Rupert, Curtis Wendlandt
Let denote the rational form of the quantized enveloping algebra associated to a complex simple Lie algebra . Let be a nonzero dominant integr…
The R-matrix formalism for quantized enveloping algebras
Sachin Gautam, Matthew Rupert, Curtis Wendlandt
Let denote the Drinfeld-Jimbo quantum group associated to a simple Lie algebra . We apply a modification of the -matrix construction for quan…
On a conjecture of Khoroshkin and Tolstoy
Andrea Appel, Sachin Gautam, Curtis Wendlandt
We prove a no-go theorem on the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal -matrix, yielding a negative answer to a conj…
The restricted quantum double of the Yangian
Curtis Wendlandt
Let be a complex semisimple Lie algebra with associated Yangian . In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts…
Poles of finite-dimensional representations of Yangians
Sachin Gautam, Curtis Wendlandt
Let be a finite-dimensional simple Lie algebra over , and let be the Yangian of . In this paper, we study the set…
The formal shift operator on the Yangian double
Curtis Wendlandt
Let be a symmetrizable Kac-Moody algebra with associated Yangian and Yangian double . An elementary result of fu…
The meromorphic R-matrix of the Yangian
Sachin Gautam, Valerio Toledano-Laredo, Curtis Wendlandt
Let g be a complex semisimple Lie algebra and Yg its Yangian. Drinfeld proved that the universal R-matrix of Yg gives rise to rational solutions of the quantum Yang-Baxter equation…
Vertex Representations for Yangians of Kac-Moody algebras
Nicolas Guay, Vidas Regelskis, Curtis Wendlandt
Using vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced af…
The -matrix presentation for the Yangian of a simple Lie algebra
Curtis Wendlandt
Starting from a finite-dimensional representation of the Yangian for a simple Lie algebra in Drinfeld's original presentation, we construct a Hopf…
Representations of twisted Yangians of types B, C, D: II
Nicolas Guay, Vidas Regelskis, Curtis Wendlandt
We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII…
Equivalences between three presentations of orthogonal and symplectic Yangians
Nicolas Guay, Vidas Regelskis, Curtis Wendlandt
We prove the equivalence of two presentations of the Yangian of a simple Lie algebra and we also show the equivalence with a third presentation whe…
Coproduct for the Yangian of an affine Kac-Moody algebra
Nicolas Guay, Hiraku Nakajima, Curtis Wendlandt
Given an affine Kac-Moody algebra, we explain how to construct a coproduct for its associated Yangian. In order to prove that this coproduct is an algebra homomorphism, we obtain,…
Representations of twisted Yangians of types B, C, D: I
Nicolas Guay, Vidas Regelskis, Curtis Wendlandt
We initiate a theory of highest weight representations for twisted Yangians of types B, C, D and we classify the finite-dimensional irreducible representations of twisted Yangians…
Twisted Yangians of small rank
Nicolas Guay, Vidas Regelskis, Curtis Wendlandt
We study quantized enveloping algebras called twisted Yangians associated with the symmetric pairs of types CI, BDI and DIII (in Cartan's classification) when the rank is small. We…