A ug 2 00 6 On block partial linearizations of the pfaffian . A . A

2 6 Fe b 20 09 On block partial linearizations of the pfaffian . A . A

Amitsur's formula, which expresses det(A + B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian of block matrices. As applications, in upcoming papers we determine generators for the SO(n)-invariants of several matrices and relations for the O(n)-invariants of several matrices over a field of arbitrary charact...

On Block Partial Linearizations of the Pfaffian

Amitsur's formula, which expresses det(A + B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian of block matrices. As applications, in upcoming papers we determine generators for the SO(n)-invariants of several matrices and relations for the O(n)-invariants of several matrices over a field of arbitrary charact...

m at h . A C ] 2 2 A ug 2 00 6 COMBINATORIAL SYMBOLIC POWERS SETH

Symbolic powers of ideals are studied in the combinatorial context of monomial ideals. When the ideals are generated by quadratic squarefree monomials, the generators of the symbolic powers are obstructions to vertex covering in the associated graph and its blow-ups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of seca...

ar X iv : m at h / 04 12 16 9 v 3 [ m at h . D G ] 2 A ug 2 00 6 TABLEAUX OVER LIE ALGEBRAS , INTEGRABLE SYSTEMS , AND CLASSICAL SURFACE THEORY

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical soliton surfaces. Completely integrable equations such as the G/G0-system of Terng...

ar X iv : h ep - e x / 04 08 01 4 v 1 6 A ug 2 00 4 Plans for Kaon Physics at BNL