Gröbner bases and determinantal ideals

Winfried Bruns , Aldo Conca

MSC 2000

05E10 Tableaux, representations of the symmetric group

13F50 Rings with straightening laws, Hodge algebras

13F55 Face and Stanley-Reisner rings; simplicial complexes

13H10 Special types

13P10 Polynomial ideals, Gröbner bases

14M12 Determinantal varieties

Abstract
We give an introduction to the theory of determinantal ideals and rings, their Groebner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras.