Stable splittings, spaces of representations and almost commuting elements in Lie groups

Almost commuting elements in compact Lie groups

On Spaces of Commuting Elements in Lie Groups

The purpose of this paper is to introduce a new method of “stabilizing” spaces of homomorphisms Hom(π,G) where π is a certain choice of finitely generated group and G is a compact Lie group. The main results apply to the space of all ordered n-tuples of pairwise commuting elements in a compact Lie group G, denoted Hom(Zn, G), by assembling these spaces into a single space for all n ≥ 0. The res...

commuting and non -commuting graphs of finit groups

فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...

Mirror symmetry, Langlands duality, and commuting elements of Lie groups

By normalizing a component of the space of commuting pairs of elements in a reductive Lie group G, and the corresponding space for the Langlands dual group, we construct pairs of hyperkähler orbifolds which satisfy the conditions to be mirror partners in the sense of Strominger-Yau-Zaslow. The same holds true for commuting quadruples in a compact Lie group. The Hodge numbers of the mirror partn...

Unitary Representations of Unimodular Lie Groups in Bergman Spaces

For an arbitrary unimodular Lie group G, we construct strongly continuous unitary representations in the Bergman space of a strongly pseudoconvex neighborhood of G in the complexification of its underlying manifold. In particular, the Bergman spaces of these manifolds are infinite-dimensional.