Areas of Interest
Algebra, Lie algebras and their representations, conformal field theory, piecewise isometry groups
Research
Finite dimensional semisimple Lie algebras, tensor product decomposition of irreducible modules, representation theory of the infinite dimensional Kac-Moody Lie algebras, bosonic and fermionic creation and annihilation operators, affine and hyperbolic Kac-Moody algebras, topics in combinatorics, power series identities, modular forms and functions, Siegel modular forms, conformal field theory, string theory, and statistical mechanical models, vertex operator algebras, their modules and intertwining operators, the theory of fusion rules, Weyl groups of Kac-Moody Lie algebras, tessellations associated with Weyl groups, piecewise isometry groups defined from Weyl group tessellations.
Ph.D. Students
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Joshua Carey,
Spring, 2022
— Branching rule decomposition of the level-1 $E_8^{(1)}$-module with respect to the irregular subalgebra $F_4^{(1)} \oplus G_2^{(1)}$
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Diego Penta,
Spring, 2016
— Decomposition of the Rank 3 Kac-Moody Lie Algebra F with Respect to the Rank 2 Hyperbolic Subalgebra Fib
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Christopher Mauriello,
Spring, 2013
— Branching Rule Decomposition of Irreducible Level-1 $E_6^{(1)}$-modules with respect to $F_4^{(1)}$
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Quincy Loney,
Summer, 2012
— Decomposition of Level-1 Representations of $D_4^{(1)}$ With Respect to its Subalgebra $G_2^{(1)}$ in the Spinor Construction
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Omar Saldarriaga,
Summer, 2004
— Fusion Algebras, Symmetric Polynomials, Orbits of Elementary N-Groups, and Rank-Level Duality
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Mike Weiner,
Spring, 1994
— Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras
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