47 citations · 89 across the 13 of their papers we have counts for
14 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…
An abelian formula for the quantum Weyl group action of the coroot lattice
S. Gautam, V. Toledano-Laredo
Let g be a complex simple Lie algebra and Uq(Lg) its quantum loop algebra, where q is not a root of unity. We give an explicit formula for the quantum Weyl group action of the coro…
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 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…
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 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…
An explicit isomorphism between quantum and classical sl(n)
Andrea Appel, Sachin Gautam
Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal envelopin…
Elliptic quantum groups and their finite-dimensional representations
Sachin Gautam, Valerio Toledano-Laredo
Let g be a complex semisimple Lie algebra, tau a point in the upper half-plane, and h a complex deformation parameter such that the image of h in the elliptic curve E_tau is of inf…
Meromorphic tensor equivalence for Yangians and quantum loop algebras
Sachin Gautam, Valerio Toledano-Laredo
Let be a complex semisimple Lie algebra, and , the corresponding Yangian and quantum loop algebra, with deformation parame…
Yangians, quantum loop algebras and abelian difference equations
S. Gautam, V. Toledano-Laredo
Let g be a complex, semisimple Lie algebra, and Y_h(g) and U_q(Lg) the Yangian and quantum loop algebra of g. Assuming that h is not a rational number and that q=exp(i πh), we cons…
Monodromy of the trigonometric Casimir connection for sl_2
Sachin Gautam, Valerio Toledano-Laredo
We show that the monodromy of the trigonometric Casimir connection on the tensor product of evaluation modules of the Yangian Ysl_2 is described by the quantum Weyl group operators…
Yangians and quantum loop algebras
Sachin Gautam, Valerio Toledano-Laredo
Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum loop algebra U_h(Lg) of g degenerates to the Yangian Y_h(g). We strengthen this result by constructing…
Cluster algebras and Grassmannians of type G2
Sachin Gautam
We prove a conjecture of Geiss, Leclerc and Schröer, producing cluster algebra structures on multi-homogeneous coordinate ring of partial flag varieties, for the case . As a c…