All Questions
17 questions
1
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55
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Combinatorial structure of the entanglement spectrum and quantum error correction in finite vector spaces
Let $V$ be a finite-dimensional vector space over $\mathbb{C}$ with dimension $d$. Consider a subspace $S \subset V^{\otimes n}$ representing the code subspace of a quantum error correcting code. We ...
- 63.9k
5
votes
1
answer
804
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Expressing symmetric function in power-sum basis
I am trying to prove the following identity
\begin{equation}
\prod_{i=1}^{m}(1-x_{i}z)^{-u}\prod_{j=1}^{n}(1-y_{i}z)^{-v} \prod_{i=1}^{m}\prod_{j=1}^{n}(1-(x_i +y_j)z)^{-w}\\ = \sum_{\lambda, \mu}c_{\...
CommunityBot
- 1
5
votes
1
answer
305
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In search of a combinatorial proof on particular set of partitions
Given a partition $\lambda=(\lambda_1\geq\lambda_2\geq\dots)$, denote the conjugate partition by $\lambda'=(\lambda_1'\geq\lambda_2'\geq\dots)$. For example, if $\lambda=(4,2,2)$ then $\lambda'=(3,3,1,...
- 5,590
12
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2
answers
1k
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Young-Fibonacci version of Nekrasov-Okounkov
This question addresses a hierarchy of linear recurrences
which arise from an attempt to generalize the Nekrasov-Okounkov
formula to the Young-Fibonacci setting.
A related posting
extensions of the ...
- 2,137
2
votes
0
answers
104
views
Cut and Join for Hurwitz number with multiple spin
Let me introduce some background of cut and join equation for spin Hurwitz number with the completed cycle as mentioned in
https://arxiv.org/pdf/1103.3120.pdf
We fix two partition $\mu $ and $\nu$ of ...
- 685
1
vote
0
answers
138
views
Conjugation of bosonic and fermionic
We use the notation from semi-infinite wedge formalism $\bigwedge^{\infty/2}V$ with vector space $V$ generated by $$\left\{\underline{s}\mid s \in \mathbb{Z}+\frac12\right\}$$,
we consider the charge ...
- 685
7
votes
1
answer
376
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Jack function in power symmetric basis
In Macdonald's book, the Jack symmetric function $J_{\lambda}(x_1,\ldots, x_n)$ for a partition $\lambda$
is defined by three properties (orthogonality, triangularity, and normalization). In the ...
- 158
3
votes
0
answers
342
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Sum of products of irreducible characters of the symmetric group over a subgroup
When trying to build a dual formulation for lattice gauge theories using Weingarten integration I am getting sums of the kind
$$I^{m, n}_{\mu, \nu} (\sigma, \tau) = \sum_{\pi \in S_n} \chi_\mu (\pi \...
9
votes
1
answer
444
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Young tableaux for exceptional Lie algebras
Irreducible representations for the $A$-series Lie algebras are labelled Young diagrams, with a basis of each given by Young tableaux. Moreover, analogues exist for the $B,C$, and $D$ series.
Does ...
- 16.5k
25
votes
3
answers
1k
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what else is in $\prod_{j=1}^n(1+q^j)$?
From time to time, I run into the finite product $\prod_{j=1}^n(1+q^j)$. And, the more it happens, the more fascinated I've become. So, herein, I wish to get help in collecting such results. To give ...
- 5,622
5
votes
1
answer
337
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partitions into odd parts vs hooks and symplectic contents
Given a partition $\lambda=(\lambda_1\geq\lambda_2\geq\dots)$, denote the conjugate partition by $\lambda'=(\lambda_1'\geq\lambda_2'\geq\dots)$. For example, if $\lambda=(4,2,2)$ then $\lambda'=(3,3,1,...
- 43.2k
14
votes
1
answer
503
views
Littlewood–Richardson rule and the Harish-Chandra-Itzykson-Zuber integral
The Littlewood–Richardson rule states that the product of two Schur polynomials can be written as a finite weighted sum of Schur polynomials. More precisely
$$
s_\lambda s_\mu = \sum_\nu c_{\lambda,\...
- 424
1
vote
0
answers
137
views
spin networks and topological states
Consider an unoriented bipartite quad-graph $\Gamma$ embedded in a a closed surface $\Sigma$ and a state space $\mathcal{H} = \bigotimes_{\text{edges}} \, \Bbb{C}_e^2$ consisting of spins
situated ...
- 2,137
4
votes
0
answers
152
views
Differences of Numbers of Helicity States in 4-dimensional Strings
The question whether the states in $D=2m + 2$ dimensional string theory,
which carry a representation of $SO(2m)$, span spaces which carry
representations of $SO(2m+1)$ seems hopelessly complicated.
...
- 155
1
vote
0
answers
229
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Semi-Standard Young Tableaux: Do Diagrams for $O(2m)$ combine to Diagrams from $O(2m+1)$?
Let $n_\lambda^K$ be the number all semi-standard Young tableaux of size
$K$ with Ferrers diagrams diagram $\lambda$
(i.e. the number of all fillings of $\lambda$ with natural numbers with weakly ...
- 188k
4
votes
1
answer
907
views
Is there a generalization of Schur - Weyl duality and plethysm for direct product of special unitary groups?
Consider the semisimple compact group $K=SU(N_1)\times SU(N_2) \times \ldots \times SU(N_S)$ acting naturally on $\mathcal{H}=\mathcal{H}_1 \otimes \mathcal{H}_2 \otimes \ldots \otimes \mathcal{H}_S$, ...
- 965
8
votes
1
answer
1k
views
Symmetric tensor product of bosonic/fermionic Hilbert space
Consider two representation of the group $SU(n)$: $Sym^k(\mathbb{C}^n)$ and $\wedge^k\mathbb{C}^n$ ($k\leq n$) and take their symmetric tensor products: $Sym^2(Sym^k(\mathbb{C}^n))$, $Sym^2(\wedge^k\...
- 965