It is shown that there is an order isomorphism φ from the poset V of B ×B-orbits on the wonderful compactification of a semi-simple adjoint group G with Weyl group W to an interval in reverse Chevalley-Bruhat order on a non-canonically associated Coxeter group Ŵ (in general neither finite nor affine). Moreover, φ preserves the corresponding Kazhdan-Lusztig polynomials. Springer’s (partly conjec...

We define certain extensions of Jacobi groups A<sub>1</sub>, prove an analogue Chevalley theorem for their invariants, and construct a Dubrovin-Frobenius structure on its orbit space.