Prove that every quotient representation of a completely reducible representation is completely reducible.
Could anyone give me a hint for this?
2026-03-25 14:34:40.1774449280
Any quotient representation of completely reducible is completely reducible.
78 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in REPRESENTATION-THEORY
- How does $\operatorname{Ind}^G_H$ behave with respect to $\bigoplus$?
- Minimal dimension needed for linearization of group action
- How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?
- Assuming unitarity of arbitrary representations in proof of Schur's lemma
- Are representation isomorphisms of permutation representations necessarily permutation matrices?
- idempotent in quiver theory
- Help with a definition in Serre's Linear Representations of Finite Groups
- Are there special advantages in this representation of sl2?
- Properties of symmetric and alternating characters
- Representation theory of $S_3$
Related Questions in INVARIANT-THEORY
- Equality of certain modules of coinvariants: $(gl(V)^{\otimes n})_{gl(V)}=(gl(V)^{\otimes n})_{GL(V)}=(gl(V)^{\otimes n})_{SL(V)}$
- Sufficient conditions for testing putative primary and secondary invariants
- Invariant-theory
- If E and F are both invariants of the assignment, any combination E⊕F will also be invariant - how to combine invariants?
- $\operatorname{dim}V^G = \operatorname{dim}(V^\ast)^G$, or $G$ linearly reductive implies $V^G$ dual to $(V^\ast)^G$
- On the right-invariance of the Reynolds Operator
- The polarization of the determinant is invariant?
- Product of two elements in a semidirect product with distinct prime powers
- Largest subgroup in which a given polynomial is invariant.
- Ring of Invariants of $A_3$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Hint : if $M$ is completely reducible, $N$ is a subrepresentation, and $K$ a subrepresentation of $M/N$, we wish to find a subrepresentation $S$ of $M/N$ such that $K\oplus S = M/N$.
If $\pi: M\to M/N$ is the projection map, what can you say about $\pi^{-1}(K)$ ? What does the hypothesis on $M$ tell us ?