Units in Hecke algebras (Q1305042)

Let \(H\) be a subgroup of a finite group \(G\) and let \(e\) be an idempotent in the group algebra \(\mathbb{C} H\) of \(H\) over the field \(\mathbb{C}\) of complex numbers. The Hecke algebra of the pair \((G,e)\) is defined by \({\mathcal H}={\mathcal H}(G,e)=e\mathbb{C} Ge\). This paper investigates conditions under which elements of a standard spanning set of \({\mathcal H}(G,e)\) are units. General criteria are developed as well as results that apply to induced linear characters, permutation representations of nilpotent groups and certain induced representations of finite groups of Lie type.