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A remarkable relation between representation theory of affine Lie algebras and models of statistical mechanics based on the Yang-Baxter equation has been discovered and intensively studied by Date et… (More)

Suppose a finite group acts on a schemeX and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify… (More)

- Alistair Savage, Sean Ferguson Tyrrel
- Bioresource technology
- 2005

Compost liquor results from the percolation of precipitation through composting waste; the release of liquids from high moisture content feedstocks; and as a result of runoff from hard surfaces and… (More)

- Alistair Savage
- 2006

For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of… (More)

- Alistair Savage
- 2006

Using subvarieties, which we call Demazure quiver varieties, of the quiver varieties of Nakajima, we give a geometric realization of Demazure modules of Kac-Moody algebras with symmetric Cartan data.… (More)

Article history: Received 23 September 2011 Available online 27 October 2011 Communicated by Peter Littelmann

- Alistair Savage
- 2006

This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of… (More)

- Alistair Savage
- 2006

Kashiwara and Saito have defined a crystal structure on the set of irreducible components of Lusztig’s quiver varieties. This gives a geometric realization of the crystal graph of the lower half of… (More)

Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules… (More)

- Alistair Savage, Oded Yacobi
- J. Comb. Theory, Ser. A
- 2015

The Grothendieck groups of the categories of finitely generated modules and finitely generated projective modules over a tower of algebras can be endowed with (co)algebra structures that, in many… (More)