STABILITY PATTERNS IN REPRESENTATION THEORY
STABILITY PATTERNS IN REPRESENTATION THEORY
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DOI：
10.1017/fms.2015.10
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发表时间：
2013-02
期刊：
影响因子：
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通讯作者：
Steven V. Sam;A. Snowden
中科院分区：
文献类型：
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作者：
Steven V. Sam;A. Snowden
我们发展了一个全面的理论，稳定的代表性类别的几个序列的群体，包括经典和对称的群体，以及他们的关系，不稳定的类别。这个理论的一个重要组成部分是稳定表示范畴和其他各种范畴之间的一系列等价关系，每个范畴都有自己的风格（表示论的，组合的，交换代数的，或范畴的），并提供了一个独特的观点稳定范畴。我们用这个理论产生了一系列具体的结果：例如，建设单射决议的简单对象，对偶之间的正交和辛理论，和一个典型的导出自等价的一般线性理论。
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is an array of equivalences between the stable representation category and various other categories, each of which has its own flavor (representation theoretic, combinatorial, commutative algebraic, or categorical) and offers a distinct perspective on the stable category. We use this theory to produce a host of specific results: for example, the construction of injective resolutions of simple objects, duality between the orthogonal and symplectic theories, and a canonical derived auto-equivalence of the general linear theory.