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- W3099040070 abstract "The boundary seam algebras mathsf{b}_{n,k}(beta=q+q^{-1}) <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msub><mml:mstyle mathvariant=sans-serif><mml:mi>𝖻</mml:mi></mml:mstyle><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false form=prefix>(</mml:mo><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mi>q</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mi>q</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=false form=postfix>)</mml:mo></mml:mrow></mml:math> were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras mathsf{b}_{n,k}(beta=q+q^{-1}) <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msub><mml:mstyle mathvariant=sans-serif><mml:mi>𝖻</mml:mi></mml:mstyle><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false form=prefix>(</mml:mo><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mi>q</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mi>q</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=false form=postfix>)</mml:mo></mml:mrow></mml:math> is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. The dimensions of the irreducible modules and of the radicals of standard ones are also given. The methods proposed here might be applicable to a large family of algebras, for example to those introduced recently by Flores and Peltola, and Crampé and Poulain d’Andecy." @default.
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- W3099040070 date "2020-02-05" @default.
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- W3099040070 title "The representation theory of seam algebras" @default.
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- W3099040070 doi "https://doi.org/10.21468/scipostphys.8.2.019" @default.
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