I am study the representation theory of the big quantum group at a root of unity, and I am wonder if it is known a complete classification of the indecomposable modules for it. To be more specific, because the general question is hard to answer, Is it known a complete classification of indecomposable modules for the big quantum group of $\mathfrak{sl}_2$ ? I know there is a classification for the small quantum group of $\mathfrak{sl}_2$, ("Indecomposable restricted representations for quantum $\mathfrak{sl}_2$, Chari & Premet), but for the big, I could't find any answer.
2026-03-25 11:08:31.1774436911
Indecomposable modules for the big quantum group
48 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 QUANTUM-GROUPS
- Verma module $V(\lambda)$ of $U_q(\mathfrak{sl}_2)$ is not simple $\implies$ $\lambda = \pm q^n$
- Structure of simple modules of $U_q(\mathfrak{sl}_2)$ at a root of unity.
- What are $q$-deformations?
- Intuition behind the relation of commutative Hopf algebra and Groups
- Definition of the Quantum plane and the Yang Baxter Equation
- Quantum invariants of 2-knots
- Integrable modules of quantum groups.
- Bogoliubov Transform
- Reference on correspondence between commutative Hopf Algebras and Groups
- What is the relation between crystals and crystal bases?
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?