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Special Unipotent Representations of Simple Linear Lie Groups of Type A
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作者 Dan BARBASCH Jia Jun MA +1 位作者 Bin Yong SUN Chen Bo ZHU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第3期707-716,共10页
Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and... Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and show in particular that all of them are unitarizable. 展开更多
关键词 Special unipotent representations unitary representations coherent continuation Weyl group representations
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Transfer of Highest Weight Modules and Small Unipotent Representations
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作者 Hai An HE Jing Song HUANG Kayue Daniel WONG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第3期772-791,共20页
We study the transfer between small special unipotent representations for all equal rank real forms of type E_(6) and E_(7). As a consequence, one can verify these modules are unitarity using the results of Wallach an... We study the transfer between small special unipotent representations for all equal rank real forms of type E_(6) and E_(7). As a consequence, one can verify these modules are unitarity using the results of Wallach and Zhu. Moreover, the K-spectra of these modules can be obtained explicitly. 展开更多
关键词 unipotent representations Wallach representations Transfer of unitary modules
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Holomorphic map with unipotent Jacobian matrices in C^3
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作者 陈志华 陈文革 《Science China Mathematics》 SCIE 2002年第2期147-154,共8页
We prove that the holomorphic unipotent Jacobian conjecture is valid when n = 3.
关键词 JACOBIAN conjecture HOLOMORPHIC unipotent map ANALYTIC variety.
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On the Deepest Fallacy in the History of Mathematics: The Denial of the Postulate about the Approximation Nature of a Simple-Iteration Method and Iterative Derivation of Cramer’s Formulas
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作者 Albert Iskhakov Sergey Skovpen 《Applied Mathematics》 2019年第6期371-382,共12页
Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonst... Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations. 展开更多
关键词 System of Linear Algebraic Equations (SLAE) NILPOTENT MATRIX unipotent MATRIX Eigenvalue Assignment Finite ITERATIVE Process Cramer’s FORMULAS
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The recognition of equivariant bifurcation problems 被引量:2
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作者 李养成 《Science China Mathematics》 SCIE 1996年第6期604-612,共9页
The orbit of an equivariant bifurcation problem with multiparameter is characterized under the action of the group of unipotent equivalences. When the unipotent tangent space is invariant under unipotent equivalences,... The orbit of an equivariant bifurcation problem with multiparameter is characterized under the action of the group of unipotent equivalences. When the unipotent tangent space is invariant under unipotent equivalences, the recognition problem can be solved by just using linear algebra. Sufficient conditions for a subspace to be intrinsic subspace under unipotent equivalences are given. 展开更多
关键词 EQUIVARIANT BIFURCATION PROBLEM intrinsic vector SUBSPACE RECOGNITION PROBLEM unipotent equivalence.
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STABILITY OF CERTAIN RINGS OF HIGHEST WEIGHT VECTORS 被引量:1
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作者 邓少强 候自新 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2001年第1期57-62,共6页
The authors prove the stability of the rings of highest weight vectors of the action of Om x GLn on the complex polynomial rings on Cm,n. As an application, the structure of the rings for m = 3 is determined.
关键词 Rational representations Maximal unipotent subgroups Rings of highest weight vectors
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Construction of complete generalized algebraic groups
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作者 WANG Dengyin 《Science China Mathematics》 SCIE 2005年第6期808-818,共11页
With one exception, the holomorph of a finite dimensional abelian connectedalgebraic group is shown to be a complete generalized algebraic group. This result on algebraic group is an analogy to that on Lie algebra.
关键词 complete algebraic groups maximal torus maximal unipotent subgroups.
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