I am currently reading D. Renard's book "Représentations de groupes réductifs p-adiques". He provides no concrete examples (which would be of great help). I found some notes by Fiona Murnaghan on the subject but they don't cover the Bernstein decomposition. I was hoping someone can point out to a reference with examples (for classical groups for instance) about this particular. Thanks in advance.
2025-01-13 18:51:36.1736794296
Examples of reductive p-adic groups representations
78 Views Asked by Hans Pohl https://math.techqa.club/user/hans-pohl/detail AtRelated Questions in REPRESENTATION-THEORY
- Conjugation preserves representation?
- linear representations, usual assumption
- Example of representation
- Simultaneously diagonalize the regular representation of C2 (+) C2 (+) C2.
- In what sense are the linear characters among the irreducible characters
- representation of sym^2(V)
- Proof that the induced class function $\theta^G$ is a character if $\theta$ is a representation on subgroup
- Character representation of right regular representation as sum of irreducible characters
- For simple $\mathbb C[G]$-modules is the representation unique
- Formulas give irreducible representation, $SL(2, \mathbb{C})$.
Related Questions in P-ADIC-NUMBER-THEORY
- Closed subgroups of $Z_{p}^{\times}$
- Valuations above $\mathbb{Q}(\alpha)$
- p-adic density of zeroes of a polynomial
- Showing that $ord_p((p^n)!) = 1 + p + \dots + p^{n-1}$
- Quotient of $\mathbb{Z}_p$ by the rational integers
- Integral closure of the p-adic integers in a finite extension of the p-adic numbers
- Reconstructing formal groups from the p-map, realizing p-maps from formal group
- Prove that $a \equiv b \mod{p^j} \iff |a-b|_{p}\leq p^{-j}$
- 'Smooth' p-adic analysis (perhaps via toposes)
- Showing the sequence of partial sums of a power series is Cauchy under the p-adic norm
Related Questions in REDUCTIVE-GROUPS
- Definition of parahoric subgroup
- Are semisimple Lie groups always reductive Lie groups?
- Double Coset Space Hausdorff?
- Is the product group of finitely many copies of the multiplicative group of positive real numbers a reductive group?
- Examples of reductive p-adic groups representations
- Definition of functions in the induced space from parabolic induction
- Group extension of $G$ by $\mathbb{G}_m$ and the Picard group.
- When does an element lie in a Levi subgroup?
- Bruhat-Tits theory: how does the normalizer act on an apartment?
- Jordan normal form in a reductive group
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity