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ResearchMy area of research is the representation theory of Lie algebras. Simply put, representation theory is concerned with determining the ways a mathematical object, such as a group or an algebra, can act linearly on a vector space while respecting the operations on the object. This subject has applications in other areas of mathematics, as well as in physics and chemistry. In fact, representation theory has proven to be a powerful tool in many areas where symmetries arise. Currently, my research interests include the representation type of algebras, specifically in conjunction with the parabolic category OS. |
PublicationsNonzero infinitesimal blocks of category OS, submitted 2009.Representation type of blocks of OS in types F4 and G2, J. Algebra 322, (2009), 3823-3838. Computational Algebra. Article An analog of Kostant's theorem for the cohomology of quantum groups , with University of Georgia VIGRE Algebra Group, Proc. Amer. Math. Soc. 138 (2010) 85-99. Article On Kostant's Theorem for Lie algebra cohomology , with University of Georgia VIGRE Algebra Group, Contemporary Math. 478 (2009), 39-60. Support varieties of Weyl modules over bad primes , with University of Georgia VIGRE Algebra Group, J. Algebra 312 Issue 2 (2007), 602-633. Article Varieties of nilpotent matrices for simple Lie algebras II: Bad primes , with University of Georgia VIGRE Algebra Group, J. Algebra 292, (2005), 6599. Article Varieties of nilpotent matrices for simple Lie algebras I: Good primes , with University of Georgia VIGRE Algebra Group, J. Algebra 280 , (2004), 719-737. Article ThesesClassifying the representation type of infinitesimal blocks of category OS . Ph.D. Dissertation, University of Georgia, 2008. ArticleHeteroclinic Orbits for a Periodic Hamiltonian System . Masters Report, Utah State University, 2001. Works in ProgressNilpotent Orbit Theory and Infinitesimal Blocks of Category OS with B. J. Cooper.The Robinson-Schensted Algorithm and Infinitesimal Blocks of Category OS , with B. J. Cooper. Kazhdan-Lusztig Cells and Infinitesimal Blocks of Category OS , with B. J. Cooper. |