## One Citation

### The representation ring of $\mathrm{SL}_2(\mathbb{F}_p)$ and stable modular plethysms of its natural module in characteristic $p$

- Mathematics
- 2022

. Let p be an odd prime and let k be a ﬁeld of characteristic p . We provide a practical algebraic description of the representation ring of k SL 2 ( F p ) modulo projectives. We then investigate a…

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### A Random Walk on the Indecomposable Summands of Tensor Products of Modular Representations of SL2 F

- MathematicsAlgebras and Representation Theory
- 2021

In this paper we introduce a novel family of Markov chains on the simple representations of SL 2 F p $\left ({\mathbb {F}_p}\right )$ in defining characteristic, defined by tensoring with a fixed…

### Plethysms of symmetric functions and representations of SL 2 (C)

- Mathematics
- 2021

Let ∇λ denote the Schur functor labelled by the partition λ and let E be the natural representation of SL2(C). We make a systematic study of when there is an isomorphism ∇λSymE ∼= ∇μSymE of…

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- Mathematics
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In this paper the reader is assumed to have taken notice of [I]. In [III] 1 we described the $lambda;, and s-, structure of the Green ring of GL(2,F p), and Sl(2,F p). We shall now construct a…

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- Mathematics
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Young tableaux and Schur functions are used to analyse the angular momentum eigenstates of multiparticle configurations. The method is based on the plethysms governing the restriction from SU(2j+1)…

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- Mathematics
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### Plethysms of symmetric functions and highest weight representations

- MathematicsTransactions of the American Mathematical Society
- 2021

Let $s_\nu \circ s_\mu$ denote the plethystic product of the Schur functions $s_\nu$ and $s_\mu$. In this article we define an explicit polynomial representation corresponding to $s_\nu \circ s_\mu$…