Name | Curtis Wendlandt |
Affiliation | University of Alberta |
Department | Mathematics |
Research Area | Representation theory |
Position | PhD student |
Office | CCIS L3-256 |
Contact | cwendlan(at)ualberta(dot)ca |
I am mathematics PhD student studying the representation theory of quantum groups under the supervision of Prof. Nicolas Guay at the University of Alberta in Edmonton, Canada.
Publications
- Coproduct for Yangians of affine Kac-Moody algebras, with Nicolas Guay and Hiraku Nakajima. Advances in Mathematics 338 (2018), 865-911. pdf.
- Representations of twisted Yangians of types B, C, D: II, with Nicolas Guay and Vidas Regelskis. Transformation Groups (in press). pdf.
- The R-matrix presentation for the Yangian of a simple Lie algebra. Communications in Mathematical Physics 363 (2018), no. 1, 289–332. pdf.
- Equivalences between three presentations of orthogonal and symplectic Yangians, with Nicolas Guay and Vidas Regelskis. Letters in Mathematical Physics (2018), doi:10.1007/s11005-018-1108-6. pdf.
- Representations of twisted Yangians of types B, C, D: I, with Nicolas Guay and Vidas Regelskis. Selecta Mathematica (N.S.), 23 (2017), no.3, 2071-2156. pdf.
- Twisted Yangians of small rank, with Nicolas Guay and Vidas Regelskis. Journal of Mathematical Physics, 57 (2016), no.4, 041703, 28 pp. pdf.
Preprints
- From Yangians to Yangian doubles. Preliminary draft available upon request.
- Vertex Representations for Yangians of Kac-Moody algebras, with Nicolas Guay and Vidas Regelskis. Submitted for publication. pdf.
Current projects
- Representations of twisted Yangians of types B, C, D: III, with Nicolas Guay and Vidas Regelskis.
- The universal meromorphic \(R\)-matrix of \(Y_\hbar(\mathfrak{g})\), with Sachin Gautam and Valerio Toledano Laredo.
- R-matrix presentation of orthogonal and symplectic quantum loop algebras and their representations, with Nicolas Guay and Vidas Regelskis.
Affine Quantum Groups Reading Seminar
Fall 2018
Time & Location: Wednesdays at 4pm, CAB 563
This is a student seminar which has the format of an informal reading course. Our goal for this semester is to give a detailed exposition to the theory of Yangians. However, we also welcome any talks related to the representation theory of quantum groups. Here is a list of past and upcoming talks (to be updated sporadically).
(09/26) M. Rupert | Lie bialgebras I: Definitions and Examples |
(10/03) M. Rupert | Lie bialgebras II: Manin triples and the Lie bialgebra double |
(10/10) C. Wendlandt | Lie bialgebras III: The graded double of the Yangian Lie bialgebra |
(10/17) C. Wendlandt | Lie bialgebras IV: Pseudo-quasitriangularity of the current algebra |
(10/24) C. Wendlandt | Lie bialgebras V: Rationality properties of the current algebra |
(10/31) | No Seminar |
(11/07) C. Wendlandt | Yangians I: Quantization and definition |
(11/14) C. Wendlandt | Yangians II: Hopf structure and \( \mathbb{C}\)-form |
(11/21) C. Wendlandt | Yangians III: PBW theorem and the Rees algebra |
(11/28) C. M. Rupert | Yangians IV: Finite-dimensional representations |
[Notes]
The seminar is organized by Matt Rupert and myself. If you are interested in giving a talk or would like to be added to our mailing list, please email me at cwendlan(at)ualberta(dot)ca.