title: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

text: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

year: 2011

title: 'Fish of New Zealand'

authors: McBreen, Liam

abstract: ‘Get off the road you lycra-clad cunt!’ 

A bond is formed with a foul-mouthed kahawai hitchhiking along Surf Highway 45. A penis-riddled espionage colours a Catholic School’s swimming sports. A group of children trek down the coast on the hunt for a washed-up whale carcass. A boat-stand attendant fetishizes a neon-lit performance artist. A Toyota Corolla cruises through Hamilton fog on its way to pick up the morning-after pill. Two feuding sisters take turns on a young boy’s lizard. 

Fish of New Zealand is a collection of short stories, constructed in shifting points of view and various formats — flash, stream-of-consciousness, instructional landscaping tips, medication fine print, email chains, and euthanasia consent forms. The collection plays out like a series of kiwiana vignettes, focusing and honing in on the unique experience of growing up in Aotearoa. The landscapes are familiar, the characters recognizable, and the tone of voice is matter-of-fact kiwi. 

Although presented as a work of fiction, most of the stories here actually took place in some shape or form — as hard as that may be to believe. They have been plucked from my childhood, teenage experiences, and glimpses into the adult world, and molded into a literary mountain range. Fish of New Zealand traverses the strange, the wry, and the grotesque, in a story collection that reads like a black sand fever dream. 

The stories in this collection are at once instantly recognizable, and yet entirely foreign. Picture the driver, cruising around the coast, who spots a kahawai without luggage and his flipper in the air. Or the disillusioned accountant in a board meeting, who floats up in a cloud of nicotine and hovers over the conference room table. The collection praises the kiwi utopia of friendly geckos and Weet-Bix cards, fresh-aired bush walks and ocean-side pōhutukawas — but doesn’t shy away from the violence hidden within its roots.

At its core, Fish of New Zealand is a personal account of growing up in Aotearoa, although I hope the reader sees themselves somewhere within this collection. It shows what it means to be a New Zealander; the lives we lead and the relationships we form. How we are shaped by the place we grow up in.

text: 'Fish of New Zealand' ‘Get off the road you lycra-clad cunt!’ 

A bond is formed with a foul-mouthed kahawai hitchhiking along Surf Highway 45. A penis-riddled espionage colours a Catholic School’s swimming sports. A group of children trek down the coast on the hunt for a washed-up whale carcass. A boat-stand attendant fetishizes a neon-lit performance artist. A Toyota Corolla cruises through Hamilton fog on its way to pick up the morning-after pill. Two feuding sisters take turns on a young boy’s lizard. 

Fish of New Zealand is a collection of short stories, constructed in shifting points of view and various formats — flash, stream-of-consciousness, instructional landscaping tips, medication fine print, email chains, and euthanasia consent forms. The collection plays out like a series of kiwiana vignettes, focusing and honing in on the unique experience of growing up in Aotearoa. The landscapes are familiar, the characters recognizable, and the tone of voice is matter-of-fact kiwi. 

Although presented as a work of fiction, most of the stories here actually took place in some shape or form — as hard as that may be to believe. They have been plucked from my childhood, teenage experiences, and glimpses into the adult world, and molded into a literary mountain range. Fish of New Zealand traverses the strange, the wry, and the grotesque, in a story collection that reads like a black sand fever dream. 

The stories in this collection are at once instantly recognizable, and yet entirely foreign. Picture the driver, cruising around the coast, who spots a kahawai without luggage and his flipper in the air. Or the disillusioned accountant in a board meeting, who floats up in a cloud of nicotine and hovers over the conference room table. The collection praises the kiwi utopia of friendly geckos and Weet-Bix cards, fresh-aired bush walks and ocean-side pōhutukawas — but doesn’t shy away from the violence hidden within its roots.

At its core, Fish of New Zealand is a personal account of growing up in Aotearoa, although I hope the reader sees themselves somewhere within this collection. It shows what it means to be a New Zealander; the lives we lead and the relationships we form. How we are shaped by the place we grow up in.

year: 2022

title: Traittore; Traduttore: Cultural integrity and translation involving Maori and other indigenous languages

authors: Roa, Tom

subjects: Ethics of translation

abstract: Traittore; Traduttore is Italian for Traitor; Translator. I argue here that translation from or into an indigenous language such as Māori is always, whatever the content and function of the source text, a political act and that, therefore, a Code of Ethics grounded in indigenous perspectives is essential if the ever-present danger of cultural betrayal is to be avoided.

text: Traittore; Traduttore: Cultural integrity and translation involving Maori and other indigenous languages Traittore; Traduttore is Italian for Traitor; Translator. I argue here that translation from or into an indigenous language such as Māori is always, whatever the content and function of the source text, a political act and that, therefore, a Code of Ethics grounded in indigenous perspectives is essential if the ever-present danger of cultural betrayal is to be avoided.

year: 2004