5 papers
Representations of twisted quantum affine algebras
Juan Camilo Arias, Vyacheslav Futorny, Kailash C. Misra
We develop the representation theory of imaginary Verma modules for twisted quantum affine algebras and construct the corresponding Kashiwara algebras. The twisted case presents su…
Highest weight modules with respect to non-standard Gelfand-Tsetlin subalgebras
Juan Camilo Arias, Oscar Morales, Luis Enrique Ramirez
In this paper we study realizations of highest weight modules for the complex Lie algebra with respect to non-standard Gelfand-Tsetlin subalgebras. We also provid…
Crystal bases for reduced imaginary Verma modules of untwisted quantum affine algebras
Juan Camilo Arias, Vyacheslav Futorny, Kailash C. Misra
We consider reduced imaginary Verma modules for the untwisted quantum affine algebras $U_q(\hat{\g})$ and define a crystal-like base which we call imaginary crystal base using the…
The Category of reduced imaginary Verma modules
Juan Camilo Arias, Vyacheslav Futorny, André de Oliveira
For an arbitrary affine Lie algebra we study an analog of the category O for the natural Borel subalgebra and zero central charge. We show that such category is semisimple having t…
Introducción a los D-módulos
Juan Camilo Arias, Camilo Rengifo
Estas notas son las memorias del cursillo dictado en el XXII Congreso Colombiano de Matemáticas en la Universidad del Cauca en Popayán - Colombia. El objetivo de este escrito es br…