Background:
I have a field called "brand" with the following mapping:

"brand": {
    "analyzer": "swedish",
    "fields": {
        "search": {
            "analyzer": "search_analyzer",
            "type": "string"
        }
    },
    "type": "string"
}

The custom search_analyer looks like this:

"analyzer": {
    "search_analyzer": {
        "filter": [
            "lowercase",
            "swedish_stop",
            "swedish_stemmer",
            "swedish_folding",
            "split_words"
        ],
        "tokenizer": "standard",
        "type": "custom"
    }
},
"filter": {
    "split_words": {
        "type": "word_delimiter"
    },
    "swedish_folding": {
        "type": "icu_folding",
        "unicodeSetFilter": "[^åäöÅÄÖ]"
    },
    "swedish_stemmer": {
        "language": "swedish",
        "type": "stemmer"
    },
    "swedish_stop": {
        "stopwords": "__swedish__",
        "type": "stop"
    }
}

Using the analyzer tool we can see that the analyzer works as expected (diactrics stripped in this case):

GET /<index>/_analyze?field=brand.search&text=Lékué
{
    "tokens": [
        {
            "end_offset": 5,
            "position": 0,
            "start_offset": 0,
            "token": "lekue",
            "type": "<ALPHANUM>"
        }
    ]
}

Also looking at the term vectors for a document with the brand set to "Lékué" looks like this:

GET /<index>/product/<id>/_termvector?fields=brand.search
{
    ...
    "found": true,
    "term_vectors": {
        "brand.search": {
            "field_statistics": {
                "doc_count": 20305,
                "sum_doc_freq": 29968,
                "sum_ttf": 29976
            },
            "terms": {
                "lekue": {
                    "term_freq": 1,
                    "tokens": [
                        {
                            "end_offset": 5,
                            "position": 0,
                            "start_offset": 0
                        }
                    ]
                }
            }
        }
    },
    "took": 1
}

To the problem:
The problem is that I can't find any documents when I search for the normalized brand "lekue".
I use the following query DSL:

GET /<index>/product/_search
{
    "query": {
        "match": {
           "brand.search": "lekue"
        }
    }
}

Which returns:
{
   ...
   "hits": {
      "total": 0,
      "max_score": null,
      "hits": []
   }
}

However if I change "lekue" to the non-normalized form "Lékué" I find the documents (2):

GET /<index>/product/_search
{
    "query": {
        "match": {
           "brand.search": "Lékué"
        }
    }
}

Response:
{
   ...
   "hits": {
      "total": 2,
      "max_score": 12.780518,
      "hits": [...]
   }
}