I have a question about computing the order of an arbitrary parabolic subgroup of an affine Weyl group $W_a$. Given a proper subset $I \subset S_a$ associated with the reflections for the fundamental alcove $A_0$, is there a formula for the order of the parabolic subgroup $W_I$ generated by $I$? How can one prove it has to be finite?
2026-03-25 23:38:20.1774481900
Order of parabolic subgroups of affine Weyl groups
121 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in AFFINE-GEOMETRY
- Prove that Newton's Method is invariant under invertible linear transformations
- Equality of affine subsets
- How do you prove that an image preserving barycentric coordinates w.r.t two triangles is an affine transformation?
- Show that $\mathcal{I}(V)$ is the product ideal of $k=\mathbb{F}_2$
- Affine Spaces Exersice
- Intersection of two affine subspaces in vector space
- Averages of side and averages of angles in a triangle
- Prove that a Balanced Incomplete Block Design with parameters $(n^2, n^2+n, n+1, n, 1)$ is a finite Affine Plane
- Proving an affine transformation preserves distance.
- Connectedness and path connectedness, of irreducible affine algebraic set in $\mathbb C^n$, under usual Euclidean topology
Related Questions in COXETER-GROUPS
- Conditions for a neat subgroup to act fixed-point free
- Cardinality of a coxeter group
- The coefficient of a root in a root system must be 0 or at least 1
- In what different terms can Coxeter systems be described?
- How to obtain uniqueness in correspondence between simple systems and positive systems?
- Conjugating the longest element of a parabolic subgroup by longest element in larger parabolic?
- Two definitions of Bruhat order on $S_n$
- Combinatorics of Coxeter Groups and lenght function
- Kazhdan-Lusztig polynomials of a Dihedral group $D_n$
- What is a Coxeter Group?
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?