Browsing 1 - Oberwolfach Preprints (OWP) by MSC "17"
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Bounded Weight Modules for Basic Classical Lie Superalgebras at Infinity
[OWP-2022-09] (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-30)We classify simple bounded weight modules over the complex simple Lie superalgebras $\mathfrak{sl}(\infty |\infty)$ and $\mathfrak{osp} (m | 2n)$, when at least one of $m$ and $n$ equals $\infty$. For $\mathfrak{osp} (m | ... -
Classification of idempotent states on the compact quantum groups Uq(2), SUq(2) and SOq(3)
[OWP-2009-08] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-02)We give a simple characterisation of those idempotent states on compact quantum groups which arise as Haar states on quantum subgroups, show that all idempotent states on quantum groups $U_q(2)$, $SU_q(2)$, and $SO_q(3) ... -
Invariant Four-forms and Symmetric Pairs
[OWP-2012-03] (Mathematisches Forschungsinstitut Oberwolfach, 2012-04-24)We give criteria for real, complex and quaternionic representations to define $s$-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of ... -
Nondegenerate Invariant Symmetric Bilinear Forms on Simple Lie Superalgebras in Characteristic 2
[OWP-2020-02] (Mathematisches Forschungsinstitut Oberwolfach, 2020-02-04)As is well-known, the dimension of the space of non-degenerate invariant symmetric bilinear forms (NISes) on any simple finite-dimensional Lie algebra or Lie superalgebra is equal to at most 1 if the characteristic of the ... -
Octonion Polynomials with Values in a Subalgebra
[OWP-2020-21] (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-22)In this paper, we prove that given an octonion algebra $A$ over a field $F$, a subring $E \subseteq F$ and an octonion $E$-algebra $R$ inside $A$, the set $S$ of polynomials $f(x) \in A[x]$ satisfying $f(R) \subseteq R$ ... -
On a Conjecture of Khoroshkin and Tolstoy
[OWP-2022-14] (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-02)We prove a no-go theorem on the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal $R$-matrix, yielding a negative answer to a conjecture of Khoroshkin and Tolstoy from ... -
On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras
[OWP-2012-14] (Mathematisches Forschungsinstitut Oberwolfach, 2012-12-04)Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\mathbb{k}$ of characteristic zero. We consider the commuting variety $\mathcal{C}(\mathfrak{u})$ of the nilradical $\mathfrak{u}$ ... -
On the Complement of the Richardson Orbit
[OWP-2010-09] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-13)We consider parabolic subgroups of a general algebraic group over an algebraically closed field $k$ whose Levi part has exactly $t$ factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup $P$ ... -
On the Lie Algebra Structure of $HH^1(A)$ of a Finite-Dimensional Algebra A
[OWP-2019-10] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-17)Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. ... -
Plethysms, replicated Schur functions and series, with applications to vertex operators
[OWP-2010-12] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-14)Specializations of Schur functions are exploited to define and evaluate the Schur functions $s_\lambda [\alpha X]$ and plethysms $s_\lambda [\alpha s_\nu(X))]$ for any $\alpha$-integer, real or complex. Plethysms are then ... -
Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
[OWP-2020-01] (Mathematisches Forschungsinstitut Oberwolfach, 2020-02-03)Noncommutative Kähler structures were recently introduced by the third author as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subsequently observed that the notion of a ... -
Tensor Representations of q(∞)
[OWP-2016-09] (Mathematisches Forschungsinstitut Oberwolfach, 2016-06-17)We introduce a symmetric monoidal category of modules over the direct limit queer superalgebra $\mathfrak{q}(\infty)$. The category can be defined in two equivalent ways with the aid of the large annihilator condition. ...