On the classification of irreducible representations of real algebraic groups

1989 ◽  
pp. 101-170 ◽  
Author(s):  
R. Langlands
Keyword(s):  
Algebraic Groups ◽  
Irreducible Representations

scholarly journals Small Degree Representations of Finite Chevalley Groups in Defining Characteristic

2001 ◽  
Vol 4 ◽  
pp. 135-169 ◽  
Author(s):  
Frank Lübeck
Keyword(s):  
Algebraic Groups ◽  
Small Degree ◽  
Irreducible Representations ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Linear Algebraic Groups ◽  
Large Rank ◽  
Projective Representations ◽  
Computer Calculations ◽  
Simply Connected

AbstractThe author has determined, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l, this bound is proportional to l3, and for rank less than or equal to 11 much higher. The small rank cases are based on extensive computer calculations.

scholarly journals REFINING THE CLASSIFICATION OF THE IRREPS OF THE 1D N-EXTENDED SUPERSYMMETRY

2008 ◽  
Vol 23 (01) ◽  
pp. 37-51 ◽  
Author(s):  
ZHANNA KUZNETSOVA ◽  
FRANCESCO TOPPAN
Keyword(s):  
Quantum Mechanics ◽  
Extended Supersymmetry ◽  
Supersymmetric Quantum Mechanics ◽  
Irreducible Representations

The linear finite irreducible representations of the algebra of the 1D N-Extended Supersymmetric Quantum Mechanics are discussed in terms of their "connectivity" (a symbol encoding information on the graphs associated to the irreps). The classification of the irreducible representations with the same fields content and different connectivity is presented up to N ≤ 8.

scholarly journals HIGHER DEFORMATIONS OF LIE ALGEBRA REPRESENTATIONS II

2020 ◽  
pp. 1-24
Author(s):  
MATTHEW WESTAWAY
Keyword(s):  
Tensor Product ◽  
Algebraic Groups ◽  
Preceding Paper ◽  
Irreducible Representations ◽  
Product Theorem ◽  
Enveloping Algebras ◽  
Frobenius Kernel ◽  
Frobenius Kernels ◽  
Lie Algebra Representations ◽  
Semisimple Algebraic Groups

Steinberg’s tensor product theorem shows that for semisimple algebraic groups, the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the preceding paper in this series, deforming the distribution algebra of a higher Frobenius kernel yielded a family of deformations called higher reduced enveloping algebras. In this paper, we prove that the Steinberg decomposition can be similarly deformed, allowing us to reduce representation theoretic questions about these algebras to questions about reduced enveloping algebras. We use this to derive structural results about modules over these algebras. Separately, we also show that many of the results in the preceding paper hold without an assumption of reductivity.

scholarly journals Representations of Algebraic Groups

1963 ◽  
Vol 22 ◽  
pp. 33-56 ◽  
Author(s):  
Robert Steinberg
Keyword(s):  
Algebraic Group ◽  
Algebraic Groups ◽  
Vector Spaces ◽  
Irreducible Representations ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Prime Field ◽  
Infinite Degree ◽  
Semisimple Algebraic Groups

Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the representations of corresponding finite simple groups. (Each algebraic group is assumed to be defined over a universal field which is algebraically closed and of infinite degree of transcendence over the prime field, and all of its representations are assumed to take place on vector spaces over this field.)

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