• Corpus ID: 244270755

Non-induced modular representations of cyclic groups

@inproceedings{Jolliffe2021NoninducedMR,
  title={Non-induced modular representations of cyclic groups},
  author={Liam Jolliffe and Robert A. Spencer},
  year={2021}
}
We compute the ring of non-induced representations for a cyclic group, Cn, over an arbitrary field and show that it has rank φ(n), where φ is Euler’s totient function — independent of the characteristic of the field. Along the way, we obtain a “pick-a-number” trick; expressing an integer n as a sum of products of p-adic digits of related integers. 

Figures from this paper

References

SHOWING 1-6 OF 6 REFERENCES

Non-Induced Representations of Finite Cyclic Groups

Let K be an algebraically closed field of characteristic 0 and let G be a finite cyclic group of order n. In this note we prove, using induction on the number of prime divisors of n, that RK(G)/I ∼=

SL2 tilting modules in the mixed case

Using the non-semisimple Temperley–Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for SL2 in the mixed case. This simultaneously generalizes the

A Course in Finite Group Representation Theory

This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text.

The modular representation algebra of a finite group

1.1. Notation and terminology. G is a finite group, with unit element e. k is a field of characteristic p. By a G-module M is meant a (/c, G)-module. Elements of G act as right operators on M, and me