SUPERSYMMETRIC HILBERT-SPACE

被引：7

作者：

ROTA, GC ^{[1
]}

STEIN, JA ^{[1
]}

机构：

[1] CALIF STATE UNIV CHICO,DEPT MATH & STAT,CHICO,CA 95929

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 1990年 / 87卷 / 02期

关键词：

algebras with straightening laws; invariant theory; skew-symmetric tensors; supersymmetric algebra; Young tableaux;

D O I：

10.1073/pnas.87.2.653

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A generalization is given of the notion of a symmetric bilinear form over a vector space, which includes variables of positive and negative signature ('supersymmetric variables'). It is shown that this structure is substantially isomorphic to the exterior algebra of a vector space. A supersymmetric extension of the second fundamental theorem of invariant theory is obtained as a corollary. The main technique is a supersymmetric extension of the standard basis theorem. As a byproduct, it is shown that supersymmetric Hilbert space and supersymplectic space are in natural duality.

引用

页码：653 / 657

页数：5