The first fundamental theorem of invariant theory for the orthosymplectic supergroup
DOI10.1007/s00220-016-2731-7zbMath1360.22027arXiv1602.04885OpenAlexW2752466779MaRDI QIDQ507177
Gustav Isaac Lehrer, Ruibin Zhang, Zhang Hechun
Publication date: 3 February 2017
Published in: Communications in Mathematical Physics, European Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1602.04885
Brauer algebraSchur-Weyl dualitytensor invariantquantum supergrouporthosymplectic supergroupsuper-Pfaffianribbon graph category
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Vector and tensor algebra, theory of invariants (15A72) Analysis on and representations of infinite-dimensional Lie groups (22E66) String diagrams and graphical calculi (18M30)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A realisation of the quantum supergroup \(U(\mathfrak{gl}_{m|n})\)
- Gradings on walled Brauer algebras and Khovanov's arc algebra
- Branes and supergroups
- The first fundamental theorem of invariant theory for the orthosymplectic supergroup
- A quantum analogue of the first fundamental theorem of classical invariant theory
- The Zhang transformation and \({\mathcal U}_q(\text{osp}(1,2l))\)-Verma modules annihilators
- The Brauer category and invariant theory
- Unitary highest weight representations of quantum general linear superalgebra
- Dual canonical bases for the quantum general linear supergroup
- Etingof-Kazhdan quantization of Lie superbialgebras
- Strongly multiplicity free modules for Lie algebras and quantum groups
- Affine walled Brauer algebras and super Schur-Weyl duality
- Canonical bases for the quantum supergroups \(\mathbf U(\mathfrak{gl}_{m|n})\)
- On endomorphisms of quantum tensor space
- The quantum general linear supergroup, canonical bases and Kazhdan-Lusztig polynomials
- A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
- Quantum field theory and the Jones polynomial
- Multiparametric quantum deformation of the general linear supergroup
- Quantum group invariants and link polynomials
- Universal \(R\)-matrix for quantized (super)algebras
- Universal R-matrices for quantum groups associated to simple Lie superalgebras
- Structure of quasitriangular quasi-Hopf algebras
- Finite-dimensional representations of \(U_ q(osp (1/2n))\) and its connection with quantum \(so(2n+1)\)
- The theory of Lie superalgebras. An introduction
- Quantization of Lie bialgebras. II, III
- Crystal bases for \(U_q(osp (1,2r))\)
- Structure and representations of the quantum general linear supergroup
- Tensor product representations for orthosymplectic Lie superalgebras
- Integrable representations of \(U_q(\text{osp}(1,2n))\)
- Braided tensor categories
- Tortile tensor categories
- Analogue of the classical invariant theory for Lie superalgebras
- A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras
- Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras.
- Character formula for infinite-dimensional unitarizable modules of the general linear super\-algebra.
- The representation theory of affine Temperley-Lieb algebras
- The first fundamental theorem of invariant theory for the orthosymplectic super group
- Ribbon graphs and their invariants derived from quantum groups
- Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
- Braided compact closed categories with applications to low dimensional topology
- The general linear supergroup and its Hopf superalgebra of regular functions.
- Quantum superalgebra representations on cohomology groups of non-commutative bundles
- Cellular algebras
- Quantization of Lie bialgebras. I
- The second fundamental theorem of invariant theory for the orthogonal group.
- Mathematical foundations of supersymmetry
- Knot polynomials and Vassiliev's invariants
- Invariants of the orthosymplectic Lie superalgebra and super Pfaffians
- Dual canonical bases for the quantum special linear group and invariant subalgebras
- Some remarks on quantized Lie superalgebras of classical type
- On the heat equation and the index theorem
- Integration on Lie supergroups: a Hopf superalgebra approach
- Crystal bases for $U_{q}(\Gamma (\sigma _{1},\sigma _{2},\sigma _{3}))$
- QUANTUM SUPERGROUPS AND SOLUTIONS OF THE YANG-BAXTER EQUATION
- THREE-MANIFOLD INVARIANTS ARISING FROM Uq(osp(1|2))
- Invariant integration on classical and quantum Lie supergroups
- A Temperley–Lieb Analogue for the BMW Algebra
- Casimir elements of ε Lie algebras
- Eigenvalues of Casimir operators for the general linear, the special linear, and the orthosymplectic Lie superalgebras
- Quantum double construction for graded Hopf algebras
- Graded tensor calculus
- Solutions of the graded classical Yang-Baxter equation and integrable models
- Classification of all star irreps of gl(m‖n)
- Cohomology of Lie superalgebras 𝔰𝔩m|nand 𝔬𝔰𝔭2|2n
- Symmetry, Representations, and Invariants
- Remarks on Classical Invariant Theory
- Generalized Gel’fand invariants and characteristic identities for quantum groups
- Universal R matrices and invariants of quantum supergroups
- Universal L operator and invariants of the quantum supergroup U q (gl(m/n))
- Braid group representations arising from quantum supergroups with arbitrary q and link polynomials
- A two-parameter quantization of osp(4/2)
- Finite dimensional irreducible representations of the quantum supergroup Uq (gl(m/n))
- QUANTUM SUPERGROUPS, LINK POLYNOMIALS AND REPRESENTATION OF THE BRAID GENERATOR
- Diagram algebras, Hecke algebras and decomposition numbers at roots of unity
- On braided tensor categories of typeBCD
- Cohomology of Lie superalgebras and their generalizations
- Quantum enveloping superalgebras and link invariants
- QUANTUM SUPERGROUPS AND TOPOLOGICAL INVARIANTS OF THREE-MANIFOLDS
- Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$
- On the structure ofUq(sl(m,1)): crystal bases
- Serre presentations of Lie superalgebras
- Lie superalgebras
- Quantum invariants of knots and 3-manifolds
- An analog of the classical invariant theory for Lie superalgebras. I, II