Ordinary and modular characters of \(\mathrm{SU}(3,p)\). (English) Zbl 0699.20032
In an earlier paper [J. Algebra 72, 8–16 (1981; Zbl 0474.20021)] the author studied the relationship between the ordinary and modular characters of the group \(\mathrm{SL}(3,p)\). In this paper he considers the special unitary group \(\mathrm{SU}(2,p)\). By a method analogous to that of [loc. cit.] he gives the decomposition of the principal indecomposable character \(U(0,0)\) corresponding to the trivial character, into ordinary irreducible characters, where \(p\geq 7\). Then he gives a table listing the decomposition behavior of the principal indecomposable characters \(U(a,b)\) in the principal block, for various values of \(a\) and \(b\), when \(p\equiv 1\pmod 3\). There is also a brief discussion of the dual problem of decomposing the ordinary irreducible characters in the principal block, on reduction mod \(p\), into modular irreducible characters.
Reviewer: B.Srinivasan
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 20C20 | Modular representations and characters |
| 20G40 | Linear algebraic groups over finite fields |
Keywords:
special unitary group; decomposition; ordinary irreducible characters; principal indecomposable characters; principal block; modular irreducible charactersCitations:
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