Journal of Lie Theory

no. 1
The Affine Closure of T*(SLn/U)
Journal of Lie Theory, Volume 35 (2025) no. 1, pp. 83-100
We show that the affine closure $\overline{T^*(\mathrm{SL}_n/U)}$ has symplectic singularities, in the sense of Beauville. In the special case $n=3$, we show that the affine closure $\overline{T^*(\mathrm{SL}_3/U)}$ is isomorphic to the closure $\overline{\mathcal{O}}_\textrm{min}$ of the minimal nilpotent orbit $\mathcal{O}_{\textrm{min}}$ in $\mathfrak{so}_8$. Moreover, the quasi-classical Gelfand-Graev action of the Weyl group $W$ on $\overline{T^*(\mathrm{SL}_3/U)}$ can be identified with the restriction to $\overline{\mathcal{O}}_\textrm{min}$ of E.\,Cartan's triality action on $\mathfrak{so}_8$.
DOI: 10.5802/jolt.1374
Classification: 20G05, 17B10, 14M15
Keywords: Symplectic singularities, triality action 
@article{JOLT_2025_35_1_a4,
     author = {B. Jia},
     title = {The {Affine} {Closure} of {T*(SL\protect\textsubscript{n}/U)}},
     journal = {Journal of Lie Theory},
     pages = {83--100},
     year = {2025},
     volume = {35},
     number = {1},
     doi = {10.5802/jolt.1374},
     zbl = {1565.20112},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1374/}
}
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B. Jia. The Affine Closure of T*(SLn/U). Journal of Lie Theory, Volume 35 (2025) no. 1, pp. 83-100. doi: 10.5802/jolt.1374

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