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In an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of type Bn. In both cases, combinatorial methods were used. Almost twenty years later, using a geometric construction based on the ideas of Macdonald, first Aguado and Araujo and then Araujo, Bigeón, and Gamondi also realized the irreducible modular representations for the Weyl groups of types An and Bn. In this paper, we extend the geometric construction based on the ideas of Macdonald to realize the irreducible modular representations of the complex reflection group of type G(m,1,n)

journal of mathematics

Irreducible Modular Representations of the Reflection Group<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>

Irreducible Modular Representations of the Reflection GroupG(m,1,n)