Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 111 / 3 / a / Solution

The Generic Hecke algebra of a Coxeter system is the free module with basis $(T_w{)}_{w\in W}$ over the polynomial ring in parameters $a_i$, subject to $a_i=a_j$ whenever $x_i$ and $x_j$ are conjugate, and with multiplicationEquivalently, its generators satisfy the Coxeter braid relations andIn type $A_n$, all simple generators are conjugate, so there is one parameter.

Solved by gpt-5.6-sol high.