Assistant Professor      Mathematics and Statistics      Auburn University, AL 36849      (334) 844-5974      huanghu (AT) auburn.edu

Areas of Interests: Matrix theory, algebraic groups and Lie groups, representation theory.

Education

Research

1. Decompositions in matrices, algebraic groups and reductive Lie groups.
   Many classical decompositions co-exist in a reductive Lie group, such as Jordan decomposition, Cartan decomposition, Polar decomposition, Bruhat decomposition, Iwasawa decomposition, Levi decomposition, etc. They disclose the structures of reductive Lie group from different directions. The connections within these decompositions reveal how different structures are embedded together. The prototypes in matrices provide intuitions and examples for general situations.



2. Group orbits and invariants.
   Given a representation of an algebraic or reductive group G on V, a parabolic subgroup P imposes certain partial order (or grading) on V. One can describe the parabolic subgroup orbits and invariants on V by studying the structure of G in accordance with the partial order. They are relative to the Bruhat decomposition, Iwasawa decomposition, quadratic forms, and some topics in representation theory.



3. Some other topics in Lie theory and matrix theory.
   

Teaching

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