Research

Publications

• K. Dahiya and E. Mukhin, On classification of finite dimensional irreducible representations of the quantum affine superalgebra of type D(2|1;x), in preparation
• E. Bodish and K. Dahiya, The dynamical Weyl group and the R-matrix for the spin representation of orthogonal quantum algebras, in preparation
• K. Dahiya and E. Mukhin, Intertwiners of representations of exceptional type quantum affine superalgebras, in preparation
• K. Dahiya and E. Mukhin, Intertwiners of representations of twisted quantum affine algebras
  J. Math. Phys. 66 (5), 2025 (Editor’s Pick)
  DOI arXiv
• K. Dahiya and E. Mukhin, Intertwiners of representations of untwisted quantum affine algebras and Yangians revisited
  J. Math. Phys. 66 (5), 2025 (Editor’s Pick)
  DOI arXiv

Invited Talks

• Mathematical Physics Seminar
  Purdue University, West Lafayette, 2025
  Talk title: R-matrices for vector representations of quantum affine algebras Notes
• Quantum Groups and Representation Theory Conference
  North Carolina State University, Raleigh, 2024
  Talk title: Intertwiners of representations of quantum affine algebras and Yangians Slides
• 14th Southeastern Lie Theory Conference
  University of Virginia, Charlottesville, 2024
  Talk title: Intertwiners of representations of quantum affine algebras and Yangians Slides

Seminar Presentations

Representation Theory Seminar, Indiana University, Indianapolis

• Finite W-Algebras (2025)
• The BRST Cohomology (2025)
• The quantum determinant for Yangian of $\mathfrak{gl}_n$ (2025)
• Transfer matrices for Yangian of $\mathfrak{gl}_n$ (2025)
• Fusion of R matrices (2025)
• MacDonald polynomials (2024)
• Howe duality and quantum Weyl group (2024)
• Crystal bases for $U_q\mathfrak{sl}_n$ and Young tableaux (2023)
• The $\mathfrak{gl}_m \times \mathfrak{gl}_n$ duality (2023)
• The Gelfand–Tsetlin algebras and representations of symmetric groups (2022)
• The Pfaffian using Grassmann variables (2022)
• Characters of representations of finite groups (2021)

K-Theory Seminar, Indiana University, Indianapolis

• Generalized cohomology of complex vector bundles (2024)

Graduate Student Seminar, Indiana University, Indianapolis

• Invariant subspaces of nilpotent operators (2025)
• Quantum computing: Shor’s algorithm (2023)
• Tilings by regular vertices (2022)
• Geometric group theory: Quasi-isometry, the Švarc–Milnor lemma (2022)
• Spectral bounds in graph theory (2021)
• Discrete Fourier transform, the convolution theorem and FFT algorithm (2021)

Professional Service

• Journal Reviewer, Transformation Groups, Volume 29, 2024
• Journal Reviewer, Journal of Mathematical Physics, Volume 64, 2023