Geodesic
Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge
Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1737-1768

Voir la notice de l'article provenant de la source EMS Press

The vertex algebra W1+∞,c​ with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer n≥1, it was conjectured in the physics literature that W1+∞,−n​ should have a minimal strong generating set consisting of n2+2n elements. Using a free field realization of W1+∞,−n​ due to Kac-Radul, together with a deformed version of Weyl's first and second fundamental theorems of invariant theory for the standard representation of GLn​, we prove this conjecture. A consequence is that the irreducible, highest-weight representations of W1+∞,−n​ are parametrized by a closed subvariety of Cn2+2n.
DOI : 10.4171/jems/292
Classification : 17-XX, 13-XX, 00-XX
Keywords: Invariant theory, vertex algebra, W1+∞​ algebra, orbifold construction, strong finite generation 
@article{JEMS_2011_13_6_a5,
     author = {Andrew R. Linshaw},
     title = {Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge},
     journal = {Journal of the European Mathematical Society},
     pages = {1737--1768},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {2011},
     doi = {10.4171/jems/292},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/292/}
}
TY  - JOUR
AU  - Andrew R. Linshaw
TI  - Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge
JO  - Journal of the European Mathematical Society
PY  - 2011
SP  - 1737
EP  - 1768
VL  - 13
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/292/
DO  - 10.4171/jems/292
ID  - JEMS_2011_13_6_a5
ER  - 
%0 Journal Article
%A Andrew R. Linshaw
%T Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge
%J Journal of the European Mathematical Society
%D 2011
%P 1737-1768
%V 13
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/292/
%R 10.4171/jems/292
%F JEMS_2011_13_6_a5
Andrew R. Linshaw. Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge. Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1737-1768. doi: 10.4171/jems/292

Cité par Sources :