Noncommutative Double Bruhat Cells and Their Factorizations
نویسندگان
چکیده
0. Introduction 1 1. Quasideterminants and Quasiminors 3 1.1. Definition of quasideterminants 3 1.2. Elementary properties of quasideterminants 4 1.3. Noncommutative Sylvester formula 5 1.4. Quasi-Plücker coordinates and Gauss LDU -factorization 5 1.5. Positive quasiminors 6 2. Basic factorizations in GLn(F) 7 3. Examples 11 3.1. A factorization in the Borel subgroup of GL3(F) 11 3.2. A factorization in GL3(F) 12 3.3. A factorization in the unipotent subgroup of GL4(F) 13 4. Double Bruhat cells in GLn(F) and their factorizations 13 4.1. Structure of GLn(F) 13 4.2. Bruhat cells and Double Bruhat cells 15 4.3. Factorization problem for noncommutative double Bruhat cells 16 5. Other factorizations in GLn(F) and the twist ψoo 23 References 26
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