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The Affine Lie Algebra sln( C ) and its Z-algebra Representation

, 2011
Jonathan D. Dunbar
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ON REPRESENTATIONS OF AFFINE COXETER GROUPS

JP Journal of Algebra, Number Theory and Applications, 2016
Summary: We present certain representations of affine Coxeter groups from which both the combinatorial and the algebraic nature of these groups are visible.
Cherniavsky, Yonah, Shwartz, Robert
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Quasi‐Affinity for Unbounded Representations

Mathematische Nachrichten, 1990
AbstractQuasi‐affinity for unbounded representations are introduced and it is shown that, if a self‐adjoint representation π is quasi‐affine to a *‐representation ϱ, then ϱ is also self‐adjoint and π and ϱ are unitarily equivalent.
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Affinity groups representation + Discussion

Human Systems Management, 1981
The multiplication of street demonstrations and violence testify to an increasing dissatisfaction of the public with traditional forms of democratic representation and parliamentary opposition. Partisan candidates are often personally unknown to their thousands of electors. Inevitably, they tend to raise emotions by stressing divisive issues and making
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Unitary Representations of the Affine Group

Journal of Mathematical Physics, 1968
The unitary representations of the affine group, or the group of linear transformations without reflections on the real line, have been found previously by Gel'fand and Naimark. The present paper gives an alternate proof, and presents several properties of the representations which will be used in a later application of this group to continuous ...
Aslaksen, Erik W., Klauder, John R.
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An Affine Representation for Transversal Geometries

Studies in Applied Mathematics, 1975
Pregeometries (matroids) whose independent sets are the partial matchings of a relation (transversal pregeometries) can be canonically imbedded in a free‐simplicial pregeometry (one whose points lie freely on flats spanned by a simplex). Conversely, all subgeometries of such free‐simplicial pregeometries are transversal.
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Etale Affine Representations of Lie Groups

1998
Let G be a finite-dimensional connected Lie group with Lie algebra g. Denote by E a real vector space and by Aff(E) the group of affine automorphisms $${\text{Aff}}\left( E \right) = \left\{ {\left( {\begin{array}{*{20}{c}} A&b \\ 0&1 \end{array}} \right)|A \in {\text{GL}}\left( E \right),{\text{ }}b \in E} \right\}$$ .
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