scholarly journals Separating invariants for multisymmetric polynomials

2020 ◽  
pp. 1
Author(s):  
Artem Lopatin ◽  
Fabian Reimers
Keyword(s):  
Separating Invariants

scholarly journals Separating invariants for modular $P$-groups and groups acting diagonally

2009 ◽  
Vol 16 (6) ◽  
pp. 1029-1036 ◽  
Author(s):  
Mara D. Neusel ◽  
Müfit Sezer
Keyword(s):  
Separating Invariants

Polarization of Separating Invariants

2008 ◽  
Vol 60 (3) ◽  
pp. 556 ◽  
Author(s):  
Jan Draisma ◽  
Gregor Kemper ◽  
David Wehlau
Keyword(s):  
Separating Invariants

Polarization of Separating Invariants

2008 ◽  
Vol 60 (3) ◽  
pp. 556-571 ◽  
Author(s):  
Jan Draisma ◽  
Gregor Kemper ◽  
David Wehlau
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Group Actions ◽  
Upper Bounds ◽  
Weyl’S Theorem ◽  
Finite Group Actions ◽  
Separating Invariants ◽  
The Difference ◽  
Special Case

AbstractWe prove a characteristic free version of Weyl’s theorem on polarization. Our result is an exact analogue ofWeyl’s theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of cheap polarization, and show that it is enough to take cheap polarizations of invariants of just one copy of a representation to obtain separating vector invariants for any number of copies. This leads to upper bounds on the number and degrees of separating vector invariants of finite groups.

scholarly journals Separating invariants

2009 ◽  
Vol 44 (9) ◽  
pp. 1212-1222 ◽  
Author(s):  
Gregor Kemper
Keyword(s):  
Separating Invariants

scholarly journals The Cohen–Macaulay property of separating invariants of finite groups

2009 ◽  
Vol 14 (4) ◽  
pp. 771-785 ◽  
Author(s):  
Emilie Dufresne ◽  
Jonathan Elmer ◽  
Martin Kohls
Keyword(s):  
Finite Groups ◽  
Separating Invariants

scholarly journals Zero-Separating Invariants for Linear Algebraic Groups

2015 ◽  
Vol 59 (4) ◽  
pp. 911-924 ◽  
Author(s):  
Jonathan Elmer ◽  
Martin Kohls
Keyword(s):  
Algebraic Group ◽  
Characteristic Zero ◽  
Elementary Proof ◽  
Algebraic Groups ◽  
Linear Algebraic Group ◽  
Null Cone ◽  
Closed Field ◽  
Unipotent Group ◽  
Linear Algebraic Groups ◽  
Separating Invariants

AbstractAbstract Let G be a linear algebraic group over an algebraically closed field 𝕜 acting rationally on a G-module V with its null-cone. Let δ(G, V) and σ(G, V) denote the minimal number d such that for every and , respectively, there exists a homogeneous invariant f of positive degree at most d such that f(v) ≠ 0. Then δ(G) and σ(G) denote the supremum of these numbers taken over all G-modules V. For positive characteristics, we show that δ(G) = ∞ for any subgroup G of GL2(𝕜) that contains an infinite unipotent group, and σ(G) is finite if and only if G is finite. In characteristic zero, δ(G) = 1 for any group G, and we show that if σ(G) is finite, then G0 is unipotent. Our results also lead to a more elementary proof that βsep(G) is finite if and only if G is finite.

scholarly journals Separating invariants for arbitrary linear actions of the additive group

2013 ◽  
Vol 143 (1-2) ◽  
pp. 207-219 ◽  
Author(s):  
Emilie Dufresne ◽  
Jonathan Elmer ◽  
Müfit Sezer
Keyword(s):  
Additive Group ◽  
Separating Invariants

scholarly journals Constructing modular separating invariants

2009 ◽  
Vol 322 (11) ◽  
pp. 4099-4104 ◽  
Author(s):  
Müfit Sezer
Keyword(s):  
Separating Invariants
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