Browsing Department of Mathematics by Author "Grantcharov, Dimitar"

Now showing items 1-8 of 8

    • BASES OF INFINITE-DIMENSIONAL REPRESENTATIONS OF ORTHOSYMPLECTIC LIE SUPERALGEBRAS 

      Williams II, Dwight Anderson (2020-06-08)
      We provide explicit bases of representations of the Lie superalgebra osp(1|2n) obtained by taking tensor products of infinite-dimensional representation and the standard representation. This infinite-dimensional representation ...

    • Cuspidal Modules Of The Lie Superalgebras Osp(1|2n) 

      Malcom, Alekzander J. (Mathematics, 2010-11-01)
      The classification of all bounded weight modules for the classical Lie superalgebras is an open question. Only recently, in fact, has the question been closed for the Lie algebras (see Mathieu). We give a differential ...

    • Exponential Tensor Modules 

      Nguyen, Khoa Hoang; 0000-0001-7556-5346 (2022-06-02)
      Representation theory of Lie algebra of a finite dimensional reductive Lie algebra g is a long-standing problem. The ultimate goal is to classify all representations of g. However. the only case only case when a complete ...

    • Quantized Enveloping Superalgebra of Type P 

      Ahmed, Saber Murad (2022-05-09)
      We introduce a new quantized enveloping superalgebra $\mathfrak{U}_q\mathfrak{p}_n$ attached to the Lie superalgebra $\mathfrak{p}_n$ of type P. The superalgebra $\mathfrak{U}_q\mathfrak{p}_n$ is a quantization of a Lie ...

    • Representations of the Extended Poincare Superalgebras in Four Dimensions 

      Griffis, John David; 0000-0002-1463-566X (2016-05-13)
      Eugene Wigner used the Poincare group to induce representations from the fundamental internal space-time symmetries of (special) relativistic quantum particles. Wigner’s students spent considerable amount of time translating ...

    • Simple Weight Modules of the Lie Algebra of Vector Fields of C2 

      Cavaness, Andrew (2017-08-14)
      Classification of the weight modules of the Lie algebra Wn of vector fields on C n has been a long-standing problem in the area of representation theory. In this thesis, a classification of all simple weight modules of W2 ...

    • Tensor Products of a Finite-Dimensional Representation and an Infinite-Dimensional Representation 

      Dewanaga, Felicia (2016-05-05)
      In this project, we explicitly find the decomposition of the tensor product of a Verma module $Z(\lambda)$ and the standard module ${\mathbb C}^n$ of the Lie algebras $\mathfrak{sl}(n)$, $n=2,3$. The result provides an ...

    • Weight Modules Of Orthosymplectic Lie Superalgebras 

      Ferguson, Thomas Lynn
      A long-standing problem in representation theory is the classification of all simple weight modules of the classical Lie superalgebras. This problem was reduced to the classification of simple bounded highest weight ...