Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part II: The Vector Finite-Dimensional Case

2018 ◽  
Vol 177 (3) ◽  
pp. 788-810 ◽  
Author(s):  
Letizia Pellegrini ◽  
Shengkun Zhu
Keyword(s):  
Image Space Analysis ◽  
Image Space ◽  
Dimensional Case ◽  
Regularity Conditions ◽  
Space Analysis ◽  
Extremum Problems ◽  
Finite Dimensional ◽  
Constrained Extremum Problems ◽  
Finite Dimensional Case

Regularity conditions for constrained extremum problems via image space

1994 ◽  
Vol 80 (1) ◽  
pp. 19-37 ◽  
Author(s):  
P. H. Dien ◽  
G. Mastroeni ◽  
M. Pappalardo ◽  
P. H. Quang
Keyword(s):  
Image Space ◽  
Regularity Conditions ◽  
Extremum Problems ◽  
Constrained Extremum Problems

scholarly journals MULTIPLE FLAG IND-VARIETIES WITH FINITELY MANY ORBITS

2021 ◽  
Author(s):  
LUCAS FRESSE ◽  
IVAN PENKOV
Keyword(s):  
Algebraic Group ◽  
Linear Algebraic Group ◽  
Interesting Case ◽  
Analogous Problem ◽  
Restrictive Condition ◽  
Dimensional Case ◽  
Essential Difference ◽  
Parabolic Subgroups ◽  
Finite Dimensional ◽  
Finite Dimensional Case

AbstractLet G be one of the ind-groups GL(∞), O(∞), Sp(∞), and let P1, ..., Pℓ be an arbitrary set of ℓ splitting parabolic subgroups of G. We determine all such sets with the property that G acts with finitely many orbits on the ind-variety X1 × × Xℓ where Xi = G/Pi. In the case of a finite-dimensional classical linear algebraic group G, the analogous problem has been solved in a sequence of papers of Littelmann, Magyar–Weyman–Zelevinsky and Matsuki. An essential difference from the finite-dimensional case is that already for ℓ = 2, the condition that G acts on X1 × X2 with finitely many orbits is a rather restrictive condition on the pair P1, P2. We describe this condition explicitly. Using the description we tackle the most interesting case where ℓ = 3, and present the answer in the form of a table. For ℓ ≥ 4 there always are infinitely many G-orbits on X1 × × Xℓ.

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