於相應與表現

Abstract

本篇介紹簡單的幾何表現理論:描繪幾何，如舒伯特多樣體、史坦堡多樣體、希爾伯特點概形，與代數，如魏爾群、黑克代數、海森堡超代數，彼此間的關聯。將一代數結構以一幾何理論之相應操作或其卷積代數來表現，可視為代數與幾何間的橋樑，以分解原理為輔，並借助雙變論作為語言。其主要動機為希望透過抽象形式化來將這些現象統一詮釋。

This report introduces some simple geometric representation theories, describing relations between geometries such as Schubert varieties, Steinberg varieties, Hilbert schemes of points and algebras like Weyl groups, Hecke algebras, Heisenberg superalgebras. These bridges are representing an algebra by operations of correspondences of a geometric theory or its convolution algebra, with auxiliary of decomposition principle, via the language of bivariant theories. The main motivation is making an attempt to develop formalisms to unify interpretations of these phenomena.