60,664 research outputs found
Spin invariant theory for the symmetric group
We formulate a theory of invariants for the spin symmetric group in some
suitable modules which involve the polynomial and exterior algebras. We solve
the corresponding graded multiplicity problem in terms of specializations of
the Schur Q-functions and a shifted q-hook formula. In addition, we provide a
bijective proof for a formula of the principal specialization of the Schur
Q-functions.Comment: v2, 17 pages, modified Introduction and updated references. v3,
correction of typos, final versio
Fermion Condensation and Gapped Domain Walls in Topological Orders
We propose the concept of fermion condensation in bosonic topological orders
in two spatial dimensions. Fermion condensation can be realized as gapped
domain walls between bosonic and fermionic topological orders, which are
thought of as a real-space phase transitions from bosonic to fermionic
topological orders. This generalizes the previous idea of understanding boson
condensation as gapped domain walls between bosonic topological orders. We show
that generic fermion condensation obeys a Hierarchy Principle by which it can
be decomposed into a boson condensation followed by a minimal fermion
condensation, which involves a single self-fermion that is its own
anti-particle and has unit quantum dimension. We then develop the rules of
minimal fermion condensation, which together with the known rules of boson
condensation, provides a full set of rules of fermion condensation. Our studies
point to an exact mapping between the Hilbert spaces of a bosonic topological
order and a fermionic topological order that share a gapped domain wall.Comment: 20 pages, 2-colum
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