- journal articles metadata
European Mathematical Society Publishing House
2024-03-19 02:52:20
4
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JCA&vol=1&iss=1&update_since=2024-03-19
Journal of Combinatorial Algebra
J. Comb. Algebra
JCA
2415-6302
2415-6310
Combinatorics
Group theory and generalizations
10.4171/JCA
http://www.ems-ph.org/doi/10.4171/JCA
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
1
2017
1
Some unitary representations of Thompson’s groups $F$ and $T$
Vaughan
Jones
Vanderbilt University, NASHVILLE, UNITED STATES
Thompson group, subfactor, conformal field theory, diffeomorphism, planar algebra, partition function, knot, link, Seifert surface
In a “naive” attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson’s groups $T$ and $F$ for any subfactor. The Thompson group elements are the “local scale transformations” of the theory. In a simple case the coefficients of the representations are polynomial invariants of links. We show that all links arise and introduce new “oriented” subgroups of $\overrightarrow F < F$ and $\overrightarrow T < T$ which allow us to produce all oriented knots and links.
Group theory and generalizations
Functional analysis
Manifolds and cell complexes
Quantum theory
1
44
10.4171/JCA/1-1-1
http://www.ems-ph.org/doi/10.4171/JCA/1-1-1
The canonical basis of the quantum adjoint representation
George
Lusztig
MIT, CAMBRIDGE, UNITED STATES
Quantum group, canonical basis, Chevalley group
We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.
Group theory and generalizations
Topological groups, Lie groups
45
57
10.4171/JCA/1-1-2
http://www.ems-ph.org/doi/10.4171/JCA/1-1-2
Kazhdan groups whose FC-radical is not virtually abelian
Mikhail
Ershov
University of Virginia, CHARLOTTESVILLE, UNITED STATES
Kazhdan's property (T), Golod–Shafarevich groups, FC-radical
We construct examples of residually finite groups with Kazhdan's property ($T$) whose FC-radical is not virtually abelian. This answer a question of Popa and Vaes about possible fundamental groups of II$_1$ factors arising from Kazhdan groups.
Group theory and generalizations
59
62
10.4171/JCA/1-1-3
http://www.ems-ph.org/doi/10.4171/JCA/1-1-3
Quantum Satake in type $A$. Part I
Ben
Elias
University of Oregon, EUGENE, UNITED STATES
Geometric Satake, quantum, Soergel bimodules, diagrammatics, webs
We give an interpretation of $\mathfrak {sl}_n$-webs as morphisms between certain singular Soergel bimodules. We explain how this is a combinatorial, algebraic version of the geometric Satake equivalence (in type $A$). We then $q$-deform the construction, giving an equivalence between representations of $U_q (\mathfrak {sl}_n)$ and certain singular Soergel bimodules for a $q$-deformed Cartan matrix. In this paper, we discuss the general case but prove only the case $n = 2, 3$. In the sequel we will prove $n \geq 4$.
Nonassociative rings and algebras
Group theory and generalizations
63
125
10.4171/JCA/1-1-4
http://www.ems-ph.org/doi/10.4171/JCA/1-1-4